It is understood that manager James McPake is expected to meet with Dundee general manager John Nelms over the next 48 hours to discuss the moves of the transfer window inside and outside the club.
The Dundee players have been absent since suffering a 2-1 loss to Aberdeen on Boxing Day. Griffiths opened the scoring that afternoon with a stunning, trademark free kick.
It was only his second goal for the club since joining Celtic on what was to be a season in September, after it was made clear to him that he was not part of the plans of the new Parkhead manager, Angel Postecoglou.
Celtic had previously triggered a 12-month contract extension. However, the player is now free to talk to other clubs about his future beyond this summer, when he becomes a free agent.
As it stands, he is expected to stay at Dundee until the end of this campaign but the Dens Park club could still decide to terminate their loan deal if they wish.
This will have to be decided over the next few days. Dundee is set to return to action with a Premiership game at Livingston on January 18.
They are already running out of options up front after Cillian Sheridan suffered a season-ending injury against St Mirren in October.
Jason Cummings, meanwhile, was reportedly told he could find a new club after a club discipline breach last month. The former Hibs forward, who is Dundee’s top scorer this season with six goals, is expected to join Griffiths in training today.