Floyd Mayweather is distancing himself from Donald Trump ... telling TMZ Sports he doesn't consider POTUS a real friend -- despite showing serious support for Trump for years. 

For the record, Floyd visited with Trump after he won the election back in November and has defended Trump's "Access Hollywood" comments as stuff a "real man" says.

So, when we saw Floyd out shopping in Bev Hills, we asked how he felt about his friend's stance on the national anthem. 

"Hold up, hold up, hold up, hold up," Floyd said ... "Friends is a strong word."

Floyd proceeded to point out some guys he considers real friends and then explained his relationship with Trump is WAY more casual. 

"I know a lot of people. I knew Barack Obama. I know Donald Trump. I know a lot of people."

But, when it comes to the his opinion on the Philadelphia Eagles and the national anthem, Floyd says he's staying mum ... "I don't want my name in no bullshit. I'm out of it."