The 36-year-old Greece international joined the Cottagers on a free transfer from Panathinaikos in September but is out of contract in the summer.
Jol told the Evening Standard: "Time is on our side, of course, because he will not go for £5m or £6m to another club.
"But, on the other hand, I do not want to see him go to other clubs. He is happy here."
Karagounis appears to have settled well in London and added: "Fulham is a great team to play for. The club have impressed me.
"To compete in the Premier League is a joy for every footballer. It is one of the toughest leagues in the world. It is better than I imagined."