The 22-year old is on loan from Championship club Wolves but his temporary spell at Easter Road comes to an end in early January.
Fenlon has seen Griffiths score 13 goals since his arrival from Molineux Stadium and hopes that a result like the Scottish Cup triumph over Edinburgh rivals Heart of Midlothian on the weekend can help lure him for the remainder of the campaign.
"Everything helps in relation to attracting players, whether it's Leigh or somebody else,” he told the Daily Record.
"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."