The 25-year-old joined the Hoops on a £2million permanent deal in summer 2012 following two very successful season-long loan deals at Parkhead.
And Forster has gone from strength-to-strength north of the border with some excellent performances, notably during last season's march to the knockout stages of the Champions League.
He has continued to produce the goods for Neil Lennon's men this term and Barcelona have already been linked with a swoop as they look to replace Victor Valdes, who is set to leave the Camp Nou at the end of the season.
City boss Manuel Pellegrini is now believed to be in the hunt for his signature as it appears he is rapidly losing patience with City's current number one Joe Hart following a serious of costly errors so far this season.
And he could look to replace him with Forster which would also be ironic given that Hart is currently ahead of the Celtic man in England boss Roy Hodgson's pecking order to be the first-choice custodian in the national side in the build up to next summer's World Cup finals in Brazil.