40-year-old Schwarzer's current deal expires this summer and Fulham have offered him an extension.
However, Jol admits that he may not be able to guarantee the Australian first-team football next season.
Jol's number two David Stockdale, who spent most of the season helping Hull City back to the Premier League, also wants to be first choice.
"We offered Mark a new deal, but the only thing is he wanted to be guaranteed to be the No 1 and that is not easy as we need a goalkeeper anyway," he said.
"We don't know what will happen to David Stockdale and he does not want to be the No 2. He wants to be No 1 as well - and that is the problem.
"We will sit down with Mark now and try to find a solution to all this."
Meanwhile, Jol praised the job done by on-loan midfielder Eyong Enoh, who is returning to Ajax after joining in January.
"Enoh has done a great job," Jol told De Telegraaf.
"He needed to adapt and this next season that will again apply to any new players."