According to the Peterborough Telegraph, the 24-year-old could part company with Posh in the coming weeks despite Darren Ferguson’s men securing promotion to the Championship this season.
It is understood that the English club have offered Dembele a bumper new deal, including a lucrative pay increase, but as yet he has not put pen to paper – and hopes of him doing so are fading fast.
The versatile forward’s current deal expires in 2022, but Peterborough could be forced to cash in on him this summer to avoid losing him for free in 12 months’ time.
Both Old Firm clubs have been linked with longstanding interests in Dembele, as have a host of English sides. Newcastle United, Sheffield United, and West Brom have all been mentioned as potential suitors since the turn of the year.
The player, who is the brother of Celtic starlet Karamoko Dembele, made headlines in January when he handed in a transfer request at the Weston Homes Stadium, but a move failed to materialise during the winter window.
However, this latest update would suggest that his exit is edging ever closer, and if he does refuse to sign the contract offer on the table then Posh will ready themselves for a bidding war to acquire his services this summer.
The club would expect a considerable fee in the millions for a player they signed from Grimsby in 2018.
Dembele registered 11 goals and 12 assists in League One this season.