Fenlon wants Griffiths stay
Brighton midfielder Andrea Orlandi has been ruled out for up to six weeks with a broken rib he suffered on Saturday.
The Spaniard, a summer signing from Swansea, suffered the injury during Saturday's 3-0 defeat at Crystal Palace.
Manager Gus Poyet told The Argus: "He has got a broken rib and he is going to be out for a while. It is going to be four to six weeks, depending on the healing process for Andrea.
"He didn't play a lot at Swansea, so we have tried to keep an eye on him because of the football he has missed in the past.
"Everything we have done until now is going to be gone. In a month-and-a-half we will have to start from zero with him, so it is very unfortunate and then, of course, there's his quality as well.
"He has been getting more influential in the team and also with set plays, so it's a blow but that is why the squad is there, to make sure we don't miss him too much."
Poyet also has injury concerns over Wayne Bridge and Adam El-Abd ahead of Saturday's trip to Charlton, while Marcos Painter is definitely ruled out and Lewis Dunk is suspended.
Griffiths has scored 13 goals for Hibs since joining on loan from Wolves at the beginning of the season, but his short-term contract expires next month.
Fenlon is keen to keep the striker beyond that deal and believes Sunday's 1-0 cup win can only help his side's cause.
He told the Daily Record: "Everything helps in relation to attracting players, whether it's Leigh or somebody else.
"We have a fantastic stadium and great training facilities. We don't have loads of money to throw at players but we have good attributes to attract them.
"And winning football matches is the biggest attribute of them all."
Griffiths was stretchered off with an ankle injury just after half-time during Sunday's win to strike a blow for Hibernian.
Fenlon's backline helped inspire the win and he reserved particular praise for Lewis Stevenson, who played out of position at full-back.
The manager added: "The back four were superb and left-back Lewis excellent."