CM Punk Rejects Logan Paul's MMA Call Out, Here's Why ...

CM Punk is finally responding to Logan Paul's big MMA call out ... and bad news -- it's a big, fat THUMBS DOWN!

Of course, Paul is looking to continue his combat sports career after that big boxing match with KSI back in November -- and the two names he's thrown out are Antonio Brown and CM Punk.

With AB's troubling legal issues, that fight seems like a long shot now ... so what about Punk?

Remember, 41-year-old Punk has two UFC fights under his belt -- and even though he lost 'em both, we're told he's a maniac in the gym ... and a lot of people would like to see him get another shot.

Paul is one of the people ... telling TMZ Sports he'd LOVE to throw down with the WWE legend and bragging, "I think I would destroy CM Punk if I'm being honest."

So, when we saw CM out in L.A. the other night -- we had to ask if he had any interest.

"No."

Bummer.

So, is it about the paycheck? Because our photog thinks there's "big money" in a Punk vs. Paul card.

"My definition of big money and everybody else's definition of big money is completely different," Punk explained.