The 30-year-old is out of contract with the Scottish Premiership side this summer.
Former Celtic player and manager Davie Hay is delighted to hear that new Hoops boss Brendan Rodgers is hoping to get Charlie Mulgrew tied down to a new contract at Parkhead, the Evening Times reports.
The defender's current deal expires in the coming months, but while the fact that a new contract had not been put on the table may have suggested that the vice-captain would be heading for the exit this summer, Rodgers has suggested that he wants to keep Mulgrew at the club next term.
And Hay has explained why keeping the 30-year-old around is such a smart move for the Bhoys.
"Charlie brings experience, he brings a versatility and he is a good player. You also have to remember that Celtic, bar a handful of senior players, have a relatively young squad and having a few senior pros in there can only be a benefit, I think," he told the Evening Times.
Mulgrew's form during the latter half of this past season arguably proved that he has an important role to play during the transition between Ronny Deila's and Rodgers' tenures.
His partnership with Erik Sviatchenko was important to the side clinching their fifth successive league title. And with the likes of the Dane, Jozo Simunovic and Dedryck Boyata all lacking huge amounts of experience, Mulgrew's presence could be hugely influential in ensuring that the team have the kind of spine going through their side that will lead them to a sixth successive league crown.