A319 Captain reported on departure experiencing engine vibration resulting in the flight crew returning to the departure airport where they landed safely.

Narrative

On takeoff from runway XX upon selecting gear lever up; loud noise and minor vibration began. Gear issue suspected. After gear; retracted and normal indications; engine issues suspected. Engine indications were normal; but noise and vibration increased or decreased with thrust changes. Noise was significant and made communications difficult. Vibration was secondary to noise.Advised ATC and landed uneventfully back at ZZZ. Emergency ground crew inspected both engines and airframe after shut down and did not note any abnormalities. We were towed to the gate. Maintenance crew inspected aircraft and discovered significant damage to number 2 engine. Suspected large bird strike with fan blade damage and blood/bird debris.We had not suspected a bird strike as there were no birds in the area; time of year; and no reports of bird activity. Because noise and vibration began at gear handle selection; we initially suspected gear issues; then moved onto engine issues.