The defender has been a key figure under Jol, but has so far declined to commit himself to the Cottagers beyond the end of this season, and his potential availability has attracted a number of suitors.
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Having said goodbye to Clint Dempsey, Mousa Dembele and Danny Murphy last summer, the Dutchman admits he is less than keen to lose another of his most important players.
“We will try to do everything we are capable of to keep him. There is a contract and the only thing for him to do is sign it,” Jol told reporters.
“With players like Brede, if they have a decent history and are playing well for their clubs, there will always be an interest from other clubs. I thought he was quite happy to stay here.
"Of course, he wanted to know the mission of the club – who is coming in because there were quite a lot of players going out.
“Then [Dimitar] Berbatov, [Mladen] Petric and [Hugo] Rodallega came in and he was happy, but now it is three months on. There is still five months left and hopefully he will put the money where his mouth is, show everyone he is happy again and sign.
“If you look at some of the players that came here, they had a lot of choices of other clubs, but they chose us,” he said. “So, I don’t think there’s a problem with our charisma.”
Fulham host Wigan at Craven Cottage on Saturday at 3pm.