The Scotland international is one of the best strikers in the Scottish Premiership, but he struggled for regular playing time last season.
Moussa Dembele was in stunning form for Celtic during the 2016-17 campaign, but Griffiths still contributed with important goals.
French striker Dembele will remain the first-choice striker for the Glasgow giants next season, meaning that Griffiths will have to play second fiddle unless manager Brendan Rodgers decides to go with two upfront on a regular basis.
Former Celtic striker and ex-agent of Griffiths, Jackson, believes that the ex-Dundee and Wolverhampton Wanderers man will not leave Celtic Park in the summer.
“I don’t think there will be any talk about Leigh leaving, though there may be about Moussa leaving,” Jackson told The Scottish Sun about Griffiths.
“Brendan Rodgers knows the score. You need two or three good strikers, and down south it’s four. Brendan’s got two exceptional ones there, and he’ll be desperate to keep them.
"If Leigh is playing, he doesn’t want to be any other place. That depends on who goes and who comes in, but I don’t think he’s ever mentioned leaving.”
As stated on Celtic’s official website, Griffiths has scored 85 goals in 143 appearances for the Glasgow giants so far in his career.