The tour, which will kick off on June 20 at Liverpool’s Echo Arena will witness the world’s first 128-man wrestling tournament.
Hinkles said: “We’ve been trying to contact CM Punk on and off for well over a year. We wanted him on the first show we did in Edinburgh in 2015.
“I’ve tried going through friends in the industry, I’ve gone through his website and sent dozens of emails but the opportunity has never been this big.
“We want to offer CM Punk $1 million dollars (£770,000) to come and join the 5 Star Wrestling tour starting June 10th.
“It’s a genuine offer. We’d love to hear back from the man himself. We want to do this with him.”
CM Punk sensationally quit WWE in January 2014 at the height of his career following a bitter fallout with WWE Chairman Vince McMahon, Triple H, and the company’s medical team.
Not long after his pro-wrestling departure he joined the world of MMA and signed a multi-fight contract with Ultimate Fighting Championship.
He made his Octagon debut until September 10, 2016, where he lost to Mickey Gall after just 2 minutes and 14 seconds via a rear naked choke.
He has not returned to the Octagon since.