Jol is hopeful the Norwegian will put pen to paper for another two years after talks with Fulham's hierarchy.
He said: "We made him a very good offer and he smiled for the first time since a couple of months ago, so I think he was quite happy.
"Hopefully he will sign that because he's never injured and always plays. He leads by example and we would love to have him here for the next couple of years.
"We pay good wages and made him a very good offer. You always hope people will be satisfied.
"I didn't see him because I don't do the negotiations but the people who do that told me he was quite happy."