The 31-year-old is reported to have trained with his Dens Park team-mates today while talks over his future were ongoing behind the scenes.
Griffiths joined the Dark Blues on final day of the summer transfer window, signing a season-long loan deal on the back of agreeing a one-year contract extension at Celtic.
That could leave the striker in limbo as it is clear he has no future under Ange Postecoglou at Celtic and is not wanted back at Parkhead this month.
Griffiths was hailed as a marquee loan signing for the Dee but he has not made the impact manager James McPake had hoped for with a return of just two goals in 14 appearances.
Dundee are currently second bottom of the Premiership just two points ahead of St Johnstone.