Jake Paul's GF Julia Rose Challenges Tommy Fury's GF, Let's Mud Wrestle!

Jake Paul and Tommy Fury might not be the only ones getting down and dirty -- the Problem Child's girlfriend, Julia Rose, tells TMZ Sports she wants to go up against TNT's lady, Molly-Mae Hague in a mud wrestling match for the ages!!!

There's been a lot of drama between the two girlfriends leading up to the Paul vs. Fury fight -- Julia publicly asked Molly if she wanted to place a friendly wager on the result, but got no response.

We caught up with Rose to see where things stood with Hague as the December 18 bout approaches ... and she said her efforts were all for naught.

"I tried having a bet," Rose told us while out in Vegas. "She didn't respond. Molly's not too confident in her man."

"Molly, let's make a bet. How confident are you in Tommy? Let's see."

Rose says the bet doesn't have to be like Jake's bet with Tommy -- which would force Fury to legally change his name to "Tommy Fumbles" for a year if he loses -- but makes it clear she's down to get something set in stone before the big event.

As for whether she'd take her beef into the ring with Molly-Mae ... Rose has an even better idea -- "We could mud wrestle."