The 31-year-old, who has been a key figure for the Cottagers since joining from FC Copenhagen in 2008, has yet to agree a new deal despite his contract expiring at the end of the season.
However, despite talks to tie the Norwegian down stalling, Jol believes Fulham should not consider cashing in this month.
“For us he's a tower of strength,” the Dutchman told the Fulham Chronicle. “It would be silly to sell him now.”
The former Ajax boss also hinted at the west London club potentially securing some "surprise" signings in the coming days.
“We would like to strengthen the squad because we lack a few players," he continued.
“The situation is that it is not a good market in January – you have all these players who are doing well, so you have to take them when they are doing badly.
“But most of them who are playing well you will have to pay over the odds for and we don’t want to do that, and we can’t do that anyway.
“We’ll have to see in this last week, maybe there will be one or two surprises. We’ll have to wait and see.
“All these clubs jump on the same players but we want to be a bit more like pioneers and adventurers, but it’s not easy.”