Punk has been invited several times by members of the group, notably Matt Jackson and Nick Jackson (The Young Bucks), but he has declined any invite to return to pro wrestling as he continues to train in MMA. While a Punk return to a wrestling ring would certainly be one of the most exciting the wrestling world could produce at the moment, it's not likely any time soon. Nor is an appearance with the Bullet Club.
As far as Hulk Hogan goes, according to Sports Illustrated, Hogan very much wanted to appear with the group at this year's WrestleKingdom 12 event back on January 4. There was a stipulation, though.
SI notes that Hogan wanted $750,000 for a one time appearance with the group. While NJPW is a growing promotion that drew it's biggest live crowd for WrestleKingdom in years back in January, that is an obscene amount of money for a one night appearance that probably wouldn't have made a big enough difference in the profits from the event to warrant the cost.
Matt Jackson spoke about a potential appearance with Hogan during an interview with SI back in September.
"I’d love to welcome Hulk in. He’s honestly my favorite wrestler of all time, so working with him in any capacity would be fun," Matt Jackson said.
Nick Jackson added, "I’d love to have him walk us down the aisle at the Tokyo Dome while the three of us play air guitar. That would be a dream come true.”
It would definitely be a cool moment, but it's clear that Hogan's price would need to come down quite a bit for this to be remotely possible. And with Hogan maneuvering for a return to WWE, don't expect this to happen anytime soon.