The striker will remain at Dundee on loan until the end of the transfer window but will then be allowed to leave Parkhead with his one-year contract set to be terminated early.
The 31-year-old faces an uncertain future after Celtic informed him of their decision last week.
The forward has netted only twice since arriving at Dundee in a season-long loan deal - with a recall clause - in August.
Speaking ahead of Tuesday's cinch Premiership visit to Livingston, McPake said: "Leigh has trained over the past few days and has been working hard, he's in the squad.
"When players like Leigh Griffiths pop up, you're always interested, our focus as a club is on (the game) at Livingston.
"The situation is what it is, I can't speak on behalf of Celtic, hopefully he goes and has a positive impact in our team.
"He's showing a desire to kick-start his career of late with that free-kick away to Aberdeen and scored in a bounce game last week against Forfar.
"That goal against Aberdeen is something Leigh has done all his career, he's a player that loves scoring goals and enjoying his football.
"When you get Griffiths scoring goals then you're getting a good player and we need to add more goals into him in the second half of the season."
Dundee have been left frustrated during the transfer window with Canadian midfielder Jay Chapman the only addition halfway through January.
McPake said: "It's been a frustrating window for us so far and Covid plays a huge part in that, it's tough as clubs try and keep a hold of players. Everyone at the club is working tirelessly to get players in.
"We are looking to strengthen all over the pitch, any business isn't getting rushed, it's important we're getting the right level of player into the building.
"Players have been identified from the start, it's taking longer to complete deals.
"It's frustrating for the management team, fans and football club."
McPake is full of respect for Livingston colleague David Martindale and added: "Davie is doing a great job at Livingston, who have had some great results already this season, so it will be a hard game for us."