Australian Schwarzer, 40, signed his last deal in January 2013 and has not given any firm indications on his future plans.
David Stockdale, meanwhile, has impressed during his loan spell at Hull as they press for promotion from the npower Championship.
Jol hopes the situation will be resolved one way or another soon. He said: "As you know we made him (Schwarzer) an offer, so that means we would like to keep him."
Asked if he had come back to the club yet, Jol added: "No".
Jol, though, knows Stockdale cannot wait forever to stake his claim for the Fulham number one jersey, the 27-year-old having had loan spells with several different clubs since joining from Darlington in 2008.
"The reality is Stockdale wants to be the number one, so I have got a little problem and it is a choice. Do you get him back and make him the number one or do you stick with your keeper?" Jol said. "Schwarzer did ever so well, so it's about making decisions.
"If I want another goalkeeper, I won't take a mug, I would like to take a good goalkeeper, and a good goalkeeper is someone who could be a number one.
"You can never guarantee a goalkeeper you are going to be number one, but I would like to get a good keeper in."
- David Stockdale