The striker's future remains up in the air after a disappointing first half of the season in the City of Discovery.
Dundee landing the Scotland international was seen as quite the coup but his goal return hasn’t replicated the initial expectation with just two in 14 matches.
Now, with the team second bottom of the cinch Premiership, they are wanting to cut Griffiths’ loan deal from Celtic short unless the terms of the loan can be renegotiated.
Ange Postecoglou all but confirmed during the week that there is not a future for the striker at Parkhead.
He said: "He'll probably be looking at opportunities elsewhere."
The 31-year-old remains part of McPake's squad. He has trained all week, scored in a recent bounce match and is in line to face Livingston when the top-flight resumes next week. But that could change.
“He scored in a game against Forfar on Tuesday night, set up two goals as well," McPake said.
“We are still in dialogue with Celtic, it is ongoing and we are awaiting clarity on that. There is dialogue going on with Celtic regarding a couple of things.”
One of those things is centre-back Osaze Urhoghide.
No team have conceded more than Dundee’s 37 goals this campaign and McPake is keen to strengthen the backline.
However, a move for the 21-year-old Celtic defender has “stalled”.
Dundee have spoken to the player, his agent and the club over a loan move. The Daily Record reports a switch to England could be more appealing to Urhoghide's representatives.
Meanwhile, a player on the cusp of departing is Jason Cummings who is close to moving to Western Sydney Wanderers in Australia.
The 26-year-old was left out of the last two squads prior to the winter break after attending an event the night before a training session ahead of a game against Hearts.
McPake said: “It is similar to [new signing] Jay Chapman in that there are a lot of hoops to jump through.
“If Jason is still a Dundee player come Tuesday then he is available to play.”
McPake also confirmed former Aberdeen striker Sam Cosgrove wants to stay in England after trying to tempt him north.