The 22-year-old striker, who is on loan from Wolves, scored his 28th goal of the season in the 2-1 win over city rivals Hearts at Tynecastle on Sunday to better Stevie Cowan's Easter Road record from 1986.
He now wants to become the first player at Hibs to reach the 30-goal mark since Alan Gordon and Jim O'Rourke in the 1972-73 season.
Griffiths, who picked up his Clydesdale Bank Premier League player of the year award at the Hilton Hotel in Glasgow on Monday night to add to his PFA Scotland young player of the year accolade, has three games left.
Hibs play Kilmarnock at Rugby Park on Wednesday night before taking on Dundee in the last Clydesdale Bank Premier league fixture of the season ahead of the visit to Hampden.
Asked if there was a part of him which wants to leave Griffiths out of the two games before the final, which the Leith club are looking to win for the first time in 111 years, the Hibs boss said: "It is a difficult scenario at the moment, he just wants to play and he is bubbly this morning again after winning his award last night.
"We have to manage him, we have to pick teams for the two games to make sure we get the best out of our two players but it is in your head sometimes that maybe it might be worth leaving him out to give him some recovery but we will wait and see, I haven't made my mind up on the team for tomorrow.
"Leigh wants to play, all he wants to do is train and play and if we could do that all day he would probably do that.
"But he has a target and obviously the more games he plays the better chances he has of getting it."