It is understood manager James McPake is set to meet with Dundee managing director John Nelms over the next 48 hours to discuss transfer window movements both in and out of the club.
The Dundee players have been off since suffering a 2-1 defeat against Aberdeen on Boxing Day. Griffiths opened the scoring that afternoon with a stunning trademark free-kick.
This was only his second goal for the club since joining from Celtic on what was intended to be a season-long in September after it was made clear to him that he was not part of new Parkhead manager Ange Postecoglou’s plans.
Celtic had earlier triggered a 12-month extension to his contract. However, the player is now free to speak 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 his loan agreement if they wish to do so.
This will need to be decided over the course of the next few days. Dundee are scheduled to return to action with a Premiership fixture at Livingston on 18 January.
They are already short on options up front after the season-ending injury sustained by Cillian Sheridan against St Mirren in October.
Jason Cummings, meanwhile, has reportedly been told he can find a new club after a breach of club discipline last month. The former Hibs striker, who is Dundee’s leading scorer this season with six goals, is expected to join Griffiths at training on Wednesday.