The 20-year-old Switzerland Under-21 international winger has recently expressed his frustration at a lack of first-team football at Craven Cottage this season as he has made just three appearances, with two of them coming from the bench.
As a result Kasami has hinted that he could look to secure a move away from Fulham in the January window in order to gain more action.
However Jol has bit back to insist that the former Palermo ace should not expect to walk into his starting line-up when there is a vast array of talent vying for places, while he wants the player to prove he is worthy of being selected.
Jol told the Chronicle: "There's other players in front of him and if he feels he should play in front of [Dimitar] Berbatov, Bryan Ruiz or Damien Duff he would have a big problem.
"He's young, like Kerim Frei and Kaca [Alex Kacaniklic], so the only thing he should do is work hard, play his games in the reserves and if he's really fed up with it we will find a solution.
"He's my player - I took him here and I believe in him - but he should keep his feet on the ground."
He added: "It's easy when you're 4-0 up and you come on. It's about when we're 1-0 up or drawing 1-1 and he turns the game and has an influence. Hopefully he will do that in the future."