The 26-year-old defender’s current contract with the club runs until 2019 and manager Rodgers is eager for him to commit his long-term future to the Hoops.
Boyata has held talks with Rodgers and chief executive Peter Lawwell, and a second round of discussions are due to take place.
He said, as quoted by the Scottish Sun: “Dedryck would go into his final year next summer, but I’d love him to stay. His representatives have spoken to Peter Lawwell and I’ve also spoken to Dedryck.
“He understands what I think, but you always have to respect the player. We will chat again.
“He is a player I rate highly and like all of the boys, he is seeing a really exciting period at Celtic. They want to be in this cycle and lots of them have signed up to be part of it.
“There is nothing yet on Dedryck’s contract, but I’d like him to extend it, very much so.”
Boyata has registered nine appearances across all competitions for the Hoops this season since he returned to action after a knee injury.
Since joining from Manchester City in the summer of 2015, Dedryck Boyata has been an integral part of Celtic side but, like many of his fellow centre-backs, Boyata has difficulty in stringing together an extended series of appearances. The Belgium international has made a brilliant performance in midweek against Bayern Munich, and there is a feeling among the fans that he makes too many of them for comfort. But Boyata is certainly worth persevering with, and should continue to make progress under Rodgers and his staff in the coming years if he can agree fresh terms.