The Blue Air flight to Bucharest burned off fuel over the Irish Sea and north Wales after taking off at 10:10 BST.
The Boeing 737 passenger plane landed safely at the airport shortly after 12:30 BST, the airport confirmed.
Passengers are still on board the aircraft, flight OB134, which is undamaged.
The pilot did not declare an emergency.
A spokesman for the airport said the plane was being refuelled ready for take-off.
The pilot called 20 minutes into the flight reporting the suspected strike.
Bird strikes usually involve airborne animals being sucked into aircraft engines during take-off and landing.
Earlier this year, academics from Swansea University and Argentina's National University of Comahue warned that bird strikes with aircraft and other man-made structures are on the increase.
A plane departing from Liverpool John Lennon Airport had to circle the skies for more than two hours following a suspected bird strike.