The 24-year-old has not enjoyed the type of season he would have wanted following his summer move from Hibernain.
He has played 19 games in all competitions, scoring one goal and registering five assists, but he has only started one Premiership game.
It is clear that Ronny Deila does not believe Allan is good enough, and they could sanction his departure this summer if a good offer is submitted.
Allan is not short of admirers, with three English clubs all keeping an eye on the attacking midfielder ahead of the summer transfer window.
Derby County, Nottingham Forest and QPR are all interested in signing the former West Brom man.
He moved to Celtic for £250,000 last summer, and the Bhoys are likely going to ask for a transfer fee of a similar amount should they let Allan go.