The American superstar has one fight remaining on his Showtime contract after defeating Manny Pacquiao but no opponent has yet been confirmed for the September encounter.
Golovkin, who is also unbeaten after 32 fights, owns WBA gold at middleweight but would be keen to drop down a weight division and force Mayweather into a thrilling scrap.
“Of course, it is my dream fight,” Golovkin said. “Obviously, Floyd, he is a great champion, with a little bit different style.
“He’s a smart guy. He does a lot of moving. My style is a little bit different, I like drama, I like a real fight, I like close fights. I want a big show with big drama!”
Golovkin’s immediate task is to defend his world championship against Willie Monroe in California on May 16.
But the Kazakhstan-born knockout specialist wants to unify the 160 pounds division by defeating the world’s premier middleweights.
He said: “Right now, my focus is on 160. My goal is to hold all the belts. I hope for a big fight with Miguel Cotto because he has the WBC title, I have the WBC interim belt, and of course I want a unification fight with [WBO champion] Andy Lee. I think he’s ready and, of course, my dream fight eventually is against Floyd.”??