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.
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."
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.
Might be worth it for Tom Cruise to reach out ...