The striker has been a bit-part player at Parkhead in recent years and was allowed out on loan to former club Dundee in the summer.
However, it is suggested the loan will be cut short at the halfway stage, with Celtic also set to sever ties with the 31-year-old midway through the contract extension he signed last year.
Ange Postecoglou kept him on for an additional 12 months but last week the Celtic manager hinted he did not see a Parkhead future for Griffiths and said: “He'll probably be looking at opportunities elsewhere."
The Sunday Mail reports that Celtic will pull the plug and exercise a clause in his one-year deal, leaving Griffiths, who has hit 230 goals across a 15-year career, a free agent.
He has previously played for Livingston, Hibs, Wolves and returned to former club Dundee on loan but has only scored twice this season.