The Fulham boss admits that the 33-year-old's fitness record will be a factor in the decision taken when Davies' contract expires in the summer after an injury-ravaged couple of seasons at Craven Cottage.
The Welsh winger was restricted to just seven appearances last campaign, but hasn't featured at all this time around after struggling to overcome a hip problem.
Jol told the Fulham Chronicle: "The thing with Simon is as long as I was here he was never fully-fit for more than two or three weeks, and that's a problem.
"When he was fit he was a wonderful player but if he's not fit we've got a problem, so we've got to sit down with him and talk about it."
Jol has offered the former Peterborough man use of the club's Motspur Park training facilities if he wants to try to regain his fitness for another contract.
The manager added: "We will look after Simon and, of course, he can stay here as long as he needs to get fit, but it's about him as well.
"He has to make his mind up about his own fitness and if he wants to play again."
Davies has made 169 appearances for Fulham since his arrival from Everton in 2007, scoring 17 goals.
Fulham last week