The 36-year-old's current contract at Craven Cottage is due to expire at the end of the ongoing campaign.
However, Jol has insisted that he does not want the veteran Greek midfielder to move anywhere on a free transfer.
"Time is on our side, of course, because he will not go for £5m or £6m to another club," the London Evening Standard quotes Jol as saying.
"But, on the other hand, I do not want to see him go to other clubs. He is happy here."
Karagounis joined the Whites last summer following a five-year stint with Panathinaikos.