diff --git a/src/flask_migrate/templates/aioflask-multidb/env.py b/src/flask_migrate/templates/aioflask-multidb/env.py
index fa6fd3a..f14bd6c 100644
--- a/src/flask_migrate/templates/aioflask-multidb/env.py
+++ b/src/flask_migrate/templates/aioflask-multidb/env.py
@@ -23,7 +23,7 @@ def get_engine(bind_key=None):
     try:
         # this works with Flask-SQLAlchemy<3 and Alchemical
         return current_app.extensions['migrate'].db.get_engine(bind=bind_key)
-    except TypeError:
+    except (TypeError, AttributeError):
         # this works with Flask-SQLAlchemy>=3
         return current_app.extensions['migrate'].db.engines.get(bind_key)
 
diff --git a/src/flask_migrate/templates/aioflask/env.py b/src/flask_migrate/templates/aioflask/env.py
index ecbd77f..3a1ece5 100644
--- a/src/flask_migrate/templates/aioflask/env.py
+++ b/src/flask_migrate/templates/aioflask/env.py
@@ -20,7 +20,7 @@ def get_engine():
     try:
         # this works with Flask-SQLAlchemy<3 and Alchemical
         return current_app.extensions['migrate'].db.get_engine()
-    except TypeError:
+    except (TypeError, AttributeError):
         # this works with Flask-SQLAlchemy>=3
         return current_app.extensions['migrate'].db.engine
 
diff --git a/src/flask_migrate/templates/flask-multidb/env.py b/src/flask_migrate/templates/flask-multidb/env.py
index ed6966f..31b8e72 100644
--- a/src/flask_migrate/templates/flask-multidb/env.py
+++ b/src/flask_migrate/templates/flask-multidb/env.py
@@ -22,7 +22,7 @@ def get_engine(bind_key=None):
     try:
         # this works with Flask-SQLAlchemy<3 and Alchemical
         return current_app.extensions['migrate'].db.get_engine(bind=bind_key)
-    except TypeError:
+    except (TypeError, AttributeError):
         # this works with Flask-SQLAlchemy>=3
         return current_app.extensions['migrate'].db.engines.get(bind_key)
 
diff --git a/src/flask_migrate/templates/flask/env.py b/src/flask_migrate/templates/flask/env.py
index f497a74..4c97092 100644
--- a/src/flask_migrate/templates/flask/env.py
+++ b/src/flask_migrate/templates/flask/env.py
@@ -19,7 +19,7 @@ def get_engine():
     try:
         # this works with Flask-SQLAlchemy<3 and Alchemical
         return current_app.extensions['migrate'].db.get_engine()
-    except TypeError:
+    except (TypeError, AttributeError):
         # this works with Flask-SQLAlchemy>=3
         return current_app.extensions['migrate'].db.engine