AZO TRACON Controller reported an aircraft cleared for a Visual Approach descended toward the wrong airport and they received a Low Altitude Alert.

Narrative

Aircraft X on a vector over 3GM roughly 8NM South of MKG; while being vectored for the RNAV Runway 06; reported MKG in sight and requested the Visual Approach instead. I asked if there was a clear line of sight to the MKG airport as they were reporting a cloud layer lower than the aircraft. The pilot responded in the affirmative and was then cleared for the Visual Approach and told to contact MKG tower. I did NOT verify if the pilot had MKG vs 3GM because the aircraft was almost directly above 3GM. Very shortly after switching the aircraft to the tower; the Low Altitude Alert went off. I attempted multiple times to inform the tower of the alert. In the meantime; Aircraft X was observed making sharp turns and descents appearing to align with runway 09 at 3GM. On roughly the 4th attempt to contact MKG via the shout line; I informed the tower that it appeared that the aircraft was short final for the wrong airport/runway. The tower acknowledged. Upon seeing the aircraft appear to climb and then turn towards the north to MKG I attempted at least 2 more times to contact MKG and verify they had positive control of the aircraft to land on the correct runway. The wrong surface warning never activated; and the data block was current with the correct runway.Even though the aircraft was directly over the airport when the visual approach clearance was issued; I should have pointed out 3GM anyway. I didn't think the pilot would mistake the airports and runways. It's common practice to point out 3GM when it's visibly between the aircraft and the intended airport; but I didn't because he was directly over it.