The 31-year-old was handed a one-year contract extension in the summer but failed to win over his new manager and was loaned to Dens Park.
Having scored just two goals in 14 appearances for the Dark Blues and with the prospect of a lengthy ban hanging over his head after allegedly kicking a firework into the crowd, Dundee are now exploring the possibility of terminating the loan, or renegotiating the terms.
Asked about Griffiths' situation, Postecoglou said there he has had no dialogue with the player, adding: "He'll probably be looking at opportunities elsewhere."
One player who will be remaining at Celtic, however, is young defender Stephen Welsh after Serie A outfit Udinese failed in a bid to loan the 21-year-old with an option to buy.
On the interest, Postecoglou added: "He's going nowhere."