The on-loan striker has been in fine form this season and was rewarded for his efforts by being named the Scottish PFA young player of the year last weekend.
Hibs are keen to retain his services but parent club Wolves have a one-year option on his contract and will decide whether he returns to Molineux.
Griffiths was reportedly back down south this week holding talks with the club but Fenlon was no clearer on the situation.
He said: "We've done as much as we can as a club and everybody knows where we stand on it and what we want to do.
"But he's a Wolverhampton player and they will decide what happens.
"I haven't spoken to anybody there to be honest and they don't have a manager at the moment so that's a difficult scenario for them.
"We have him on loan and we would be delighted to have him for another season if possible but we will just wait and see where that one goes."
Regardless of what the future holds for Griffiths, Fenlon would love to see him on the scoresheet against city rivals Hearts on Sunday, having netted against them earlier in the season.
He added: "He is a Hibs fan so it's probably a little bit more extra special for Hibs supporters to be scoring against their biggest rivals. We'd love to see him do that at the weekend if possible."