Speculation about a showdown between the five-weight boxing world champion Mayweather and UFC's biggest name has been rife in recent weeks.
Mayweather, 40, has previously stated he would only return to the ring to fight the Irishman and he has now given the clearest indication yet that the bout is a real possibility.
Speaking in Liverpool on the latest leg of his UK tour, Mayweather revealed: "I'm officially out of retirement for Conor McGregor, today.
"If he's really real, like he's says he is, if you really want to fight, just sign the paper.
"Conor McGregor, stop blowing smoke up everyone's a**e, if you want to fight, let's make the fight happen."
McGregor has already obtained a boxing licence granted by the California State Athletic Commission, which would allow him to box in the US state as part of a potential cross-sport fight, but he remains contracted to the UFC.
Mayweather retired in September 2015 with a 49-0 record while McGregor became UFC's first simultaneous two-weight champion in November when he beat Eddie Alvarez to claim the lightweight belt.