Griffiths played for the Dens Park outfit between 2009 and 2011, scoring 34 goals in 62 appearances before moving to Wolves for £150,000, and a return to the club ten years on is looking increasingly likely as all parties move to secure a deal.
The Scotland internationalist is a former teammate of Dundee boss James McPake, the pair having played together at both Livingston and Hibs, with McPake captaining the Easter Road side during the striker's 39-goal loan spell.
Griffiths signed a one-year extension to his Celtic contract earlier in the summer, but has been unable to break into the first team under new boss Ange Postecoglou. It is understood that the player is keen to make a return to Dundee.
He had been previously linked with a move to Hibs, which has been mooted throughout the summer, but those rumours were quashed by Easter Road boss Jack Ross last weekend after speculation intensified that Griffiths would be a makeweight in a Celtic transfer involving Hibs forward Kevin Nisbet.
Ross described rumours linking Griffiths with a return as “nonsense” adding: "It just shows how something can be created and people can run with it. As far as we're concerned there's absolutely no truth in it."
It now looks like Dundee will be a likely destination for the 31-year-old, who needs to get his career back on track after several months on the sidelines.