However, if he is given assurances over the amount of game-time he will get next season from Brendan Rodgers, Jackson thinks that there is nowhere Griffiths would rather be than Celtic Park.
Jackson has no doubt in his mind that the Celtic striker would be a success if one day he should end up playing in the English Premier League.
And when it was put to him that Griffiths’ goalscoring heroics at Hampden will mean a heightened profile for him down south, Jackson said: “It does. Maybe people down south, even in the way commentators such as Gary Neville were speaking about him, maybe sit up and take notice.
“However, if the wee man is in the Celtic team, then I don’t think he wants to be anywhere else.
“He backs himself to be better than anyone. He doesn’t think he’s better than any other striker at the club, but he’ll back himself.
“He says: ‘If you’ll play me, I’ll score goals.’ That’s where he backs himself. He has never been arrogant or blasé, it’s just belief. He’s actually a quiet boy, but he does have a surge and a belief that he can score goals.
“I don’t see him on the pitch being cocky or speaking to defenders. He just has an inner belief that he can score goals. He doesn’t strut about the pitch, sticking his chest out and saying: ‘Look at me, what a player.’
“I just think he scores goals and that’s all he wants to do in his head.
“I don’t think there will be any talk about Leigh leaving, although there may be about Moussa [Dembele] leaving.
“Brendan Rodgers knows the score. You need at least two or three good strikers, and down south it’s four.
“He’s got two exceptional ones there, and I think he’ll be desperate to keep them.
“If Leigh is playing, he doesn’t want to be any other place than Celtic. That depends on who goes and who comes in, but I don’t think he’s ever mentioned leaving.
“Even when he wasn’t in the team, he can maybe appreciate that when he was scoring all the goals the season before, there were other strikers champing at the bit to get a game.
“When Moussa was scoring a lot of goals last season he found himself out of the team, and he found that quite hard, but when he gets in Leigh does what it says on the tin.
“Leigh scores goals, and I think he could score goals in any company.
“People talk about if he could go down south and score goals, but that’s what he does.”