Coach Nathan Buckley has signalled that a raft of changes are imminent at Collingwood, with Darren Jolly and Alan Didak among those already shown the door, and Shaw's name has been firmly in the spotlight.
Guilty of some ill-disciplined acts in last Saturday's surprise elimination final loss to Port Adelaide, there has been plenty of speculation over Shaw's future at the Magpies.
Heath's brother Rhyce Shaw had his own troubles at the Pies before he was traded to the Swans in 2008, where he has enjoyed a stellar career revival, capped by last year's premiership victory over Hawthorn.
Bolton, who will retire at the end of this season following 15 seasons with the Swans, said another Shaw would be warmly welcomed in the Harbour City.
"Heath is an unbelievable player and the Swans would love to have his talents at the club," Bolton told AFL.com.au.
"I don't know exactly the process at the moment, we'll wait and see.
"It's one of those things we'll see once the season finishes.
"But there's obviously been a few grumblings down at Collingwood, so we'll work that out."
The Swans have a long history of bringing in players from other clubs and transforming their careers.
Ted Richards, Craig Bolton, Marty Mattner and Josh Kennedy are among a long list of successful Swans plucked from opposition sides.
Another player that has blossomed in Sydney is ruckman Shane Mumford, who was signed from Geelong in 2009 and remains off contract at season's end.
Bolton believes convincing Mumford to remain a Swan is crucial for the club moving forward.
"Absolutely. The ruck combination between him and Pykey (Mike Pyke) at the moment has been fantastic," he said.
"That's an important signing for the club to knock over."
The news on Thursday that Adam Goodes had been ruled out for the season came as a blow to the whole playing group and Bolton in particular.
They have spent their entire careers together and Bolton is devastated he won't have a chance to line up alongside him again.
"It's just disappointing," Bolton said. "I'm shattered I won't be able to run out on the field with him again, but that's part of footy.
"We've seen a lot of guys try to push for selection and miss out and that's what happens and we move on.
"But it's just been an honour to have a very close seat watching Adam Goodes do his thing.
"He's a phenomenal athlete and he'll end up in the Hall of Fame down the track and to see him win two Brownlows has been unbelievable."
The Swans have made some changes this week, with Ben McGlynn (calf) and Gary Rohan (omitted) making way for Harry Cunningham and Shane Biggs.
Bolton is confident the injection of pace Cunningham and Biggs provide will help ensure his career continues beyond Saturday night's semi-final against Carlton.
The 33-year-old also believes the club he will leave behind is well placed to enjoy plenty more success in the future.
"I think it is yeah. We've got guys that have played a lot of footy together," he said.
"It's great to see Dan Hannebery play his hundredth game this week. He's so young but he's played and stood up in a lot of big games.
"You've got guys like Josh Kennedy, Kieren Jack, Jarrad McVeigh's obviously still very young as well – even though he's got an old head on him.
"The future is really bright."
Twitter: @AFL_JD
