"So now that CM punk is out of his contracts and wants to do MMA. Why not me? He already said he fight me," Frank wrote on Instagram. "I got this on video from a fan. Come on CM punk we could make this a awesome fight. Plus his weight is way down. This is a recent pic. I'll make any weight to make this happen!!"
Frank, 40, won five MMA fights in a row in 2010, but hasn't competed inside the cage in close to four years.
He was supposed to face Shawn Machado on July 22, 2011 at Legacy FC 7, but the fight never materialized.
As for Punk, the WWE standout has no cage-fighting experience, but he trains with BJJ legend Rener Gracie.
Punk also hinted in a recent interview with MMA Fighting reporter Ariel Helwani that he would be interested in trying his hand at a UFC fight.
"I have this notoriety and I have this presence, so do you put that on a small show or do you start off in the UFC? Maybe I just get guzzled. Who knows? But think of all the people who want to see me get my ass kicked!" Punk told Helwani. "Think about that. So it's a really interesting question I think.
"It's like what do you do with that? Do you put me in a UFC Octagon and does that do a good buyrate because people are interested in seeing it, or do people just want to see me get beat up? And either way everyone makes a bunch of money. I get punched in the face four nights a week, and I'm not saying it's any easier or any harder than what I do. There's similarities and there's differences."
CM Punk is currently under contract with the WWE, but he walked away from the promotion following an argument he had with WWE head honcho Vince McMahon at the 2014 WWE Royal Rumble.
Punk was apparently annoyed that the WWE scripted Batista to win the Royal Rumble, rather than him.