Golovkin, aged 35, was left disappointed with the scoring of last weekend's draw against Saul 'Canelo' Alvarez but his longevity could yet match Mayweather's, despite their paths never crossing inside the ring.
"There's a reason [Mayweather] fought Conor McGregor and would never entertain fighting GGG at 154lbs," Golovkin's promoter Tom Loeffler said.
"Out of respect to Floyd, he is the only fighter that Gennady would have come to 154 for.
"There were never serious talks. We can't blame Floyd because he was never in the [middleweight] division. If he was in the division it would be a different story but he's never fought at 160lbs.
"Floyd said it would be 'easy work' because GGG has 'no special effects' but realistically they know what the outcome would have been."
Golovkin's "priority" is to rematch Canelo next May yet the IBF, WBC and WBA 'super' middleweight champion could still emulate Mayweather by fighting into his 40s.
"He said he could fight for another five years," Loeffler said. "Gennady's style of punching power doesn't diminish, like we saw with George Foreman. The power-punching is [the attribute] that goes last, with an older fighter.
"Gennady's defence is vastly underrated. He's the one coming forwards and pressing the action but [after the Canelo fight] it didn't look like he was in a 12 round fight. No swollen or black eyes, just a few scratches.
"With the right motivation, this style would allow him to fight for as long as he wants. We just saw Wladimir Klitschko fight until he was 41, Floyd fought until he was 40. We could easily see Gennady fight for the next five years - but he won't stay in the sport longer than he needs to."
Golovkin would be open to a second fight in the UK, after beating Kell Brook last September.
"Absolutely, if there's a big fight that makes sense we would consider it," Loeffler said. "We've been trying to fight Billy Joe Saunders for a while. But Gennady has crossed over into being one of the most marketable boxers in the US."
Miguel Cotto would "definitely" be considered as an opponent for Golovkin in December, should they opt to fight before a potential rematch with Canelo.
"A legend like Cotto is a shoo-in for the Hall of Fame," Loeffler said. "This is the type of fight that would motivate Gennady."