The club's leading goalscorer is on loan at Easter Road from Wolverhampton Wanderers, but his contract with the Championship strugglers is due to expire in the summer, meaning that he would become a free agent.
Despite accepting that he may go on to join a bigger club, midfielder Stevenson is hoping that Hibs can convince the 22-year-old to stay put.
"Leigh loves the club and that'll be a big factor when he's choosing where his future lies," he told the Daily Record.
"He's enjoying it up here, he's obviously settled and he knows the city, having been brought up here.
"We've got a few things in our favour to hopefully keep him but if a big club comes in, you can't blame him."
Griffiths has found the net on 25 occasions this season.