diff --git a/neutron/plugins/ml2/drivers/ovn/mech_driver/ovsdb/ovn_client.py b/neutron/plugins/ml2/drivers/ovn/mech_driver/ovsdb/ovn_client.py
index df27972f45e..9bdbf07f9ac 100644
--- a/neutron/plugins/ml2/drivers/ovn/mech_driver/ovsdb/ovn_client.py
+++ b/neutron/plugins/ml2/drivers/ovn/mech_driver/ovsdb/ovn_client.py
@@ -1473,11 +1473,13 @@ class OVNClient(object):
         """Return chassis for scheduling gateway router.
 
         Criteria for selecting chassis as candidates
-        1) chassis from cms with proper bridge mappings
-        2) if no chassis is available from 1) then,
-           select chassis with proper bridge mappings
-        3) Filter the available chassis accordingly to the routers
+        1) Chassis from cms with proper bridge mappings only (that means these
+           gateway chassis with the requested physical network).
+        2) Filter the available chassis accordingly to the routers
            availability zone hints (if present)
+
+        If the logical router port belongs to a tunnelled network, there won't
+        be any candidate.
         """
         # TODO(lucasagomes): Simplify the logic here, the CMS option has
         # been introduced long ago and by now all gateway chassis should
@@ -1486,15 +1488,13 @@ class OVNClient(object):
         cms = cms or self._sb_idl.get_gateway_chassis_from_cms_options()
         chassis_physnets = (chassis_physnets or
                             self._sb_idl.get_chassis_and_physnets())
-        cms_bmaps = []
-        bmaps = []
+        candidates = set()
         for chassis, physnets in chassis_physnets.items():
-            if physnet and physnet in physnets:
-                if chassis in cms:
-                    cms_bmaps.append(chassis)
-                else:
-                    bmaps.append(chassis)
-        candidates = cms_bmaps or bmaps or cms
+            if (physnet and
+                    physnet in physnets and
+                    chassis in cms):
+                candidates.add(chassis)
+        candidates = list(candidates)
 
         # Filter for availability zones
         if availability_zone_hints:
@@ -1505,11 +1505,8 @@ class OVNClient(object):
                           if az in utils.get_chassis_availability_zones(
                               self._sb_idl.lookup('Chassis', ch, None))]
 
-        if not cms_bmaps:
-            LOG.debug("No eligible chassis with external connectivity"
-                      " through ovn-cms-options for %s", physnet)
-        LOG.debug("Chassis candidates for scheduling gateway router ports: %s",
-                  candidates)
+        LOG.debug('Chassis candidates for scheduling gateway router ports '
+                  'for "%s" physical network: %s', physnet, candidates)
         return candidates
 
     def _get_physnet(self, network):
diff --git a/neutron/tests/functional/services/ovn_l3/test_plugin.py b/neutron/tests/functional/services/ovn_l3/test_plugin.py
index fbaa0b8aded..4f4cd90c781 100644
--- a/neutron/tests/functional/services/ovn_l3/test_plugin.py
+++ b/neutron/tests/functional/services/ovn_l3/test_plugin.py
@@ -32,12 +32,14 @@ from neutron.tests.functional.resources.ovsdb import events
 
 
 class TestRouter(base.TestOVNFunctionalBase):
-    def setUp(self):
-        super(TestRouter, self).setUp()
+    def setUp(self, **kwargs):
+        super().setUp(**kwargs)
         self.chassis1 = self.add_fake_chassis(
-            'ovs-host1', physical_nets=['physnet1', 'physnet3'])
+            'ovs-host1', physical_nets=['physnet1', 'physnet3'],
+            enable_chassis_as_gw=True, azs=[])
         self.chassis2 = self.add_fake_chassis(
-            'ovs-host2', physical_nets=['physnet2', 'physnet3'])
+            'ovs-host2', physical_nets=['physnet2', 'physnet3'],
+            enable_chassis_as_gw=True, azs=[])
         self.cr_lrp_pb_event = events.WaitForCrLrpPortBindingEvent()
         self.sb_api.idl.notify_handler.watch_event(self.cr_lrp_pb_event)
 
@@ -91,12 +93,14 @@ class TestRouter(base.TestOVNFunctionalBase):
             self.assertCountEqual(expected, chassis)
 
     def _check_gateway_chassis_candidates(self, candidates,
-                                          router_az_hints=None):
+                                          router_az_hints=None,
+                                          physnet='physnet1'):
         # In this test, fake_select() is called once from _create_router()
         # and later from schedule_unhosted_gateways()
         ovn_client = self.l3_plugin._ovn_client
+        net_type = 'vlan' if physnet else 'geneve'
         ext1 = self._create_ext_network(
-            'ext1', 'vlan', 'physnet1', 1, "10.0.0.1", "10.0.0.0/24")
+            'ext1', net_type, physnet, 1, "10.0.0.1", "10.0.0.0/24")
         # mock select function and check if it is called with expected
         # candidates.
 
@@ -127,12 +131,11 @@ class TestRouter(base.TestOVNFunctionalBase):
 
     def test_gateway_chassis_with_cms_and_bridge_mappings(self):
         # Both chassis1 and chassis3 are having proper bridge mappings,
-        # but only chassis3 is having enable-chassis-as-gw.
-        # Test if chassis3 is selected as candidate or not.
+        # but only chassis1 is having enable-chassis-as-gw.
+        # Test if chassis1 is selected as candidate or not.
         self.chassis3 = self.add_fake_chassis(
-            'ovs-host3', physical_nets=['physnet1'],
-            other_config={'ovn-cms-options': 'enable-chassis-as-gw'})
-        self._check_gateway_chassis_candidates([self.chassis3])
+            'ovs-host3', physical_nets=['physnet1'], azs=[])
+        self._check_gateway_chassis_candidates([self.chassis1])
 
     def test_gateway_chassis_with_cms_and_no_bridge_mappings(self):
         # chassis1 is having proper bridge mappings.
@@ -166,12 +169,10 @@ class TestRouter(base.TestOVNFunctionalBase):
         # Test if chassis3 is selected as candidate or not.
         self.chassis3 = self.add_fake_chassis(
             'ovs-host3', physical_nets=['physnet1'],
-            other_config={'ovn-cms-options': 'enable-chassis-as-gw'},
-            azs=['ovn'])
+            azs=['ovn'], enable_chassis_as_gw=True)
         self.chassis4 = self.add_fake_chassis(
             'ovs-host4', physical_nets=['physnet1'],
-            other_config={'ovn-cms-options': 'enable-chassis-as-gw'},
-            azs=['ovn2'])
+            azs=['ovn2'], enable_chassis_as_gw=True)
         self._check_gateway_chassis_candidates([self.chassis3],
                                                router_az_hints=['ovn'])
 
@@ -181,11 +182,9 @@ class TestRouter(base.TestOVNFunctionalBase):
         # AvailabilityZoneNotFound. after create will delete if.
         # add chassis4 is having azs [ovn2], not match routers az_hints [ovn]
         self.chassis3 = self.add_fake_chassis(
-            'ovs-host3', physical_nets=['physnet1'],
-            other_config={'ovn-cms-options': 'enable-chassis-as-gw'})
+            'ovs-host3', physical_nets=['physnet1'], enable_chassis_as_gw=True)
         self.chassis4 = self.add_fake_chassis(
-            'ovs-host4', physical_nets=['physnet1'],
-            other_config={'ovn-cms-options': 'enable-chassis-as-gw'},
+            'ovs-host4', physical_nets=['physnet1'], enable_chassis_as_gw=True,
             azs=['ovn2'])
         ovn_client = self.l3_plugin._ovn_client
         ext1 = self._create_ext_network(
@@ -213,6 +212,11 @@ class TestRouter(base.TestOVNFunctionalBase):
         # Test if chassis1 is selected as candidate or not.
         self._check_gateway_chassis_candidates([self.chassis1])
 
+    def test_gateway_chassis_no_physnet_tunnelled_network(self):
+        # The GW network is tunnelled, no physnet defined --> no possible
+        # candidates.
+        self._check_gateway_chassis_candidates([], physnet=None)
+
     def test_gateway_chassis_least_loaded_scheduler(self):
         # This test will create 4 routers each with its own gateway.
         # Using the least loaded policy for scheduling gateway ports, we
diff --git a/neutron/tests/unit/plugins/ml2/drivers/ovn/mech_driver/test_mech_driver.py b/neutron/tests/unit/plugins/ml2/drivers/ovn/mech_driver/test_mech_driver.py
index e1782669263..6953b091edb 100644
--- a/neutron/tests/unit/plugins/ml2/drivers/ovn/mech_driver/test_mech_driver.py
+++ b/neutron/tests/unit/plugins/ml2/drivers/ovn/mech_driver/test_mech_driver.py
@@ -2635,24 +2635,27 @@ class TestOVNMechanismDriver(TestOVNMechanismDriverBase):
                     return ch
         ovn_client._sb_idl.lookup = fake_lookup
 
-        # The target physnet and availability zones
-        physnet = 'public'
-        az_hints = ['az0', 'az2']
-
+        # List of chassis and chassis:physnet mappings.
+        physnet_name = 'public'
         cms = [ch0.name, ch1.name, ch2.name, ch3.name, ch4.name, ch5.name]
-        ch_physnet = {ch0.name: [physnet], ch1.name: [physnet],
-                      ch2.name: [physnet], ch3.name: [physnet],
+        ch_physnet = {ch0.name: [physnet_name], ch1.name: [physnet_name],
+                      ch2.name: [physnet_name], ch3.name: [physnet_name],
                       ch4.name: ['another-physnet'],
                       ch5.name: ['yet-another-physnet']}
 
-        candidates = ovn_client.get_candidates_for_scheduling(
-            physnet, cms=cms, chassis_physnets=ch_physnet,
-            availability_zone_hints=az_hints)
-
-        # Only chassis ch0 and ch2 should match the availability zones
-        # hints and physnet we passed to get_candidates_for_scheduling()
-        expected_candidates = [ch0.name, ch2.name]
-        self.assertEqual(sorted(expected_candidates), sorted(candidates))
+        # The target physnets, the availability zones and the expected
+        # candidates.
+        results = [{'physnet': physnet_name, 'az_hints': ['az0', 'az2'],
+                    'expected_candidates': [ch0.name, ch2.name]},
+                   {'physnet': None, 'az_hints': ['az0', 'az2'],
+                    'expected_candidates': []},
+                   ]
+        for result in results:
+            candidates = ovn_client.get_candidates_for_scheduling(
+                result['physnet'], cms=cms, chassis_physnets=ch_physnet,
+                availability_zone_hints=result['az_hints'])
+            self.assertEqual(sorted(result['expected_candidates']),
+                             sorted(candidates))
 
     def test__get_info_for_ha_chassis_group_as_extport(self):
         net_attrs = {az_def.AZ_HINTS: ['az0', 'az1', 'az2']}