Floyd Mayweather Wants to Promote Justin Bieber vs. Tom Cruise Fight

Every blockbuster fight needs a big-time promoter ... and Floyd Mayweather tells TMZ Sports he's the guy for Justin Bieber's potential fight against Tom Cruise!!

As we previously reported ... there have been serious talks about setting up a fight between the 25-year-old singer and the 57-year-old movie superstar after Biebs playfully tweeted about wanting a piece of TC last month. 

Dana White -- who was tagged in Bieber's initial post about the dream fight -- has said he'd be down to make it happen and predicts it would be the biggest fight in UFC history.

Enter Mayweather -- who says he wants NOTHING to do with training either celeb for the possible fight ... but wants EVERYTHING to do with the money involved.

"If they bring me in as a promoter, then I can talk about it. But until then, I gotta stay in my lane. Gotta stay in my business."

Remember, Mayweather used to be super tight with Justin Bieber -- he even let the pop star walk him to the ring for a few of his fights. Floyd even trained Bieber to box at one point.  

But, the two had a falling out back in 2017 ... and haven't really spoken since. 

Floyd didn't back Justin when we spoke with him ... but he didn't exactly praise him either.