After 25-year-old Bieber tagged the UFC president in a twitter post last week calling out 56-year-old Tom Cruise, White says he blew it off initially ... until he got some phone calls from "real guys" connected to the superstars.

Dana wouldn't say who he spoke with but was clear they're legit -- and they told Dana both Tom and Justin "really wanna do this fight and they believe that Tom Cruise would do the fight."

"I told them that if that's true -- and everybody involved really wants to do it -- we can talk."

In fact, White says if there's real interest from both stars "I'd be an IDIOT not to make this fight!"

And, to all the doubters, Dana says he didn't think there was a chance Floyd Mayweather vs. Conor McGregor would ever evolve into a real fight ... but that happened, right?!

Remember, Justin Bieber has trained with Floyd -- who once said the singer has enough fighting talent to be a pro boxer.

And, Tom Cruise was a star wrestler in high school -- and has a reputation for being one of the toughest actors in Hollywood who's been doing his own stunts for decades.

So, if they do agree to a fight ... it could be very interesting.

White adds, "That would be the easiest fight to promote in the history of my career."

After sending the tweet, Bieber said the whole thing was a joke ... but hey, people can change their minds.