The Hoops are understood to be closing in on a return for the shot-stopper, who is due to undergo a medical later today, according to The Sun.
Celtic have reportedly agreed a deal with English Premier League side Southampton for the goalkeeper's return to Glasgow, five years after he left for the south coast.
The 31-year-old is set to compete for the gloves at Parkhead after falling down the pecking order at St Mary's. Saints boss Ralph Hasenhuttl prefers Angus Gunn and Alex McCarthy as his two first-team options, and is believed to have given Forster the green light to leave.
Celtic boss Neil Lennon is on the look-out for a 'keeper after No.1 Scott Bain dislocated his thumb last week, leaving the Hoops with just Craig Gordon and youngster Conor Hazard as goalkeeping options.
Gordon played in the 2-1 extra-time win over Dunfermline in the Betfred Cup on Saturday but Lennon is targeting a more experienced gloveman to challenge for the No.1 spot.
Forster joined Celtic initially on loan from Newcastle before signing a permanent deal and winning three league titles with the champions. He was capped by England during his time in Glasgow and although he impressed following his move south of the Border, he fell out of favour under Mauricio Pellegrino and has effectively been playing back-up ever since.
And social media chatter suggests the towering goalie could be unveiled as a Celtic player during tonight's European showdown with AIK.