And Melbourne has emerged as a potential suitor for Shaw the day after the Magpies and the backman's management confirmed they were exploring a fresh start for the 27-year-old at a new club after a frustrating end to his season.
Club president Eddie McGuire said on Wednesday said both parties believed that looking at outside opportunities was "best for everybody and the long-term relationships".
But he said the Pies would try to mend thing with Shaw if an appropriate deal wasn't reached in next month's trade period.
"'Shawry' has a two-year contract at Collingwood, so if deals aren't on the table that aren't right for Collingwood nor are they right for him, everyone comes back together and says, 'Come on, let's work this out', then there's an opportunity," McGuire told Triple M.
"But the first step on this is to see if there is a deal to be done for 'Shawry' to go somewhere else and for Collingwood to get a good deal out of it."
The Demons are interested in Shaw's services, new football operations manager Josh Mahoney confirmed.
"It's interesting what Heath has said and the Collingwood Football Club has said in recent days," Mahoney told SEN.
"Like every club, we meet daily in list management and we go through it and Heath Shaw's name has been brought up.
"He's a very good player and he'd make our team a lot better so we'll certainly look at the opportunity to get Heath."
Shaw's season ended in disappointing circumstances when his frustration boiled over against Port Adelaide in the Pies' losing elimination final.
He gave away a free kick after a Power goal that gifted a second major to Angus Monfries.
Then, just after the siren for half-time rang, he threw the ball at Monfries' head.
Coach Nathan Buckley denied his relationship with Shaw had influenced the decision for both parties to see what offers were out there.
"We've got a pretty strong relationship," Buckley told Channel Nine's Footy Classified on Tuesday night.
"I've been open and honest with Heater over the last couple of years as senior coach and a couple of years before that as assistant. He's under no illusions where he sits.
"The decision to have a look elsewhere has been made and now we have to find an arrangement that suits both parties.
"I think it just comes to that point in time where the relationship reaches a point where you go one way or another.
"Heater's pretty keen to explore his options and the club the same."
McGuire said there was no questioning Shaw's popularity within the club and both parties were "being mature" about the decision to consider trade.
"He's an All Australian player, a premiership player, a fantastic bloke, he's charismatic, everyone loves him and it's the moment in time of where we are," he said.
Despite Shaw's ability, Buckley said the decision was in the best interests of both parties.
"He's an established name and his name is synonymous with the history of the club, but in the end we're making the right decisions for the future of the club and for our best chances of success.
"Heater's making the call for his career. That's the professional age we live in."
Shaw's older brother Rhyce benefited from a trade from Collingwood to the Sydney Swans at the end of 2008. He has since played in a premiership and has added 99 games to his career tally.