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."
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