Everton boss Roberto Martinez has said he is not looking to replace Samuel Eto'o before the end of the transfer window.
Dundee United defender Keith Watson has joined Hibernian on loan until the end of the season.
Jol's future at Craven Cottage has been the subject of intense speculation after an indifferent start to the season.
Some fans called for the head of the Dutchman after disappointing results at home to West Brom and Cardiff, but the pressure was eased on Jol following last weekend's win over Stoke.
Kasami has broken into the first-team this season after a spell on loan at Lucerne last term and he is keen to repay the faith shown in him by Jol.
"I understand the frustration from the fans, but the manager doesn't deserve [the stick]," Kasami told the Fulham Chronicle.
"He's got great experience and he's coached at some top clubs. He gave me a lot of confidence and I've tried to repay him with my performances."
The 21-year-old is happy with his form so far this season, but admits he still has a lot to learn.
"I'm one of the youngest in the team and I try to show every week what I can do," added Kasami.
"I'm very pleased with this season because I've been playing a lot and showed a lot of people that I can be an important player for Fulham."