The Hoops midfielder looks set for a Parkhead exit this summer.
Galatasaray Director of Football Cenk Ergun is due in Glasgow this week to finalise a deal for Stefan Johansen, according to the Daily Record.
The Norwegian has been linked with the Turkish giants for much of the summer and this latest development indicates their keenness for his signature.
Celtic's Stefan Johansen in action with Rangers' Dominic Ball
Johansen is in the final year of his contract and will be able to talk to clubs in January about leaving on a free next summer so Celtic must decide whether or not to cash in now.
The 25-year old enjoyed a strong debut campaign at Parkhead but has since failed to live up to his early promise and could be allowed to leave this summer for around £1.5 million.
New Celtic manager Brendan Rodgers during the press conference
Brendan Rodgers recently spoke of his desire to retain the Norwegian, in quotes published by the Daily Record, but conceded that the decision might be out of his hands.
“I have only known him this last week and a half and he has been excellent…we shall see what happens. It is speculation but he is a player I’d like to keep for sure,” said the Hoops boss.
Ross County's Ian McShane (L) in action with Celtic's Stefan Johansen
“The club has to protect itself also. If a player clearly doesn’t want to be at a club and had a year to go, the market will tell you that you have to sell that player.”
Celtic aren’t short of options in midfield and with a host of young talents coming through who may well be better suited to Rodgers’ style of play, losing Johansen shouldn’t be a massive blow.