The 31-year-old has not made the impact many were hoping for when he returned to the club having enjoyed a very good spell at Dens Park earlier in his career.
The Courier reports that the club have a break clause in the loan deal but they only have a certain period of time in which to activate it.
Speaking on Thursday, McPake said a decision would be made on Friday.
“We are in discussions at the minute regarding that as a club internally and externally with Celtic as well,” he said.
The striker is heading for his worst goal return since his first season in professional football when he netted once in four appearances for Livingston in 2006/07.
Since the 2008/09, Griffiths has hit double figures in 11 of 13 seasons coming into this campaign. But from the incredible 40-goal haul, his season tallies have been 18, 13, six, 12, seven and currently two.
In the previous six league campaigns, Griffiths has been in the top ten for shots per 90 minutes. He’s led the league in four of them, averaging more than four a game.
He is 14th with 2.6 shots per 90, albeit with Dundee and not Celtic.