Frank Mir, bottom, sees Alistair Overeem suffering the same fate he did against Brock Lesnar. Jon Kopaloff/Getty Images

Las Vegas -- Frank Mir is predicting a comeback win for an old rival of his.

The former champ is currently preparing for a rematch against Antonio Rodrigo Nogueira, scheduled for Dec. 10. Later that month, another high profile heavyweight bout takes place between Brock Lesnar and Alistair Overeem at UFC 141.

Mir, who is 1-1 in two fights with Lesnar, believes his former opponent holds a fairly significant edge against Overeem.

“Honestly, I think Brock will win pretty easily,” Mir told ESPN.com.

“I think we’re going to see the closest thing to a grappler versus striker match you’ll see nowadays. Brock is going to cover up; maybe throw one jab. He’ll rush Overeem to the cage, reach down for a leg and rip him down.”

After that happens, Mir has little faith Overeem is capable of working to his feet. One of the greatest concerns on the Dutch striker, despite the fact he’s held titles in multiple organizations, is his effectiveness fighting from the bottom.

“I don’t think he’s going to get off his back,” Mir said. “I’d be very shocked -- I’d applaud Overeem if he got off his back.”

Mir fell victim to that very thing in his second fight against Lesnar at UFC 100. He took a lot of damage off his back in the first two rounds of that fight, eventually losing via TKO.

Since the loss, Mir has certainly addressed that hole in his game. He’s worked extensively with Utah-based grappling coach Ricky Lundell, even offering him a room in his family’s home during camps.

His wrestling showed marked improvement in a decision win over Roy Nelson in May. Mir is now 3-1 in his last four fights and likely just one or two victories away from a shot at reclaiming the title.

Frank Mir's improved wrestling skills were on display against Roy Nelson. Ed Mulholland/ESPN.com

Current heavyweight champion Cain Velasquez will look to make his first title defense against Junior Dos Santos at the UFC on Fox event Nov. 12. Although Mir likes Velasquez’s chances of retaining the belt, he sees it as a 50-50 fight.

“I’m edging towards the champion, but I wouldn’t be surprised if Dos Santos pulls it off,” he said. “It might just come down to who makes the first mistake.”

As far as the idea of rekindling his old rivalry with Lesnar, of course Mir says a fight against someone you’ve lost to is always tempting. But as far as the personal beef the two had towards one another, he’s let that go.

“Time heals all wounds,” Mir said.

“And in reality, I played that up because at that time in my life I thought being loud and saying those things would be good marketing for a third fight. In the last couple years I’ve realized, if people are going to dislike me, I want it to be because of my personality and not because of something I did for marketing a fight.”