A number of clubs are thought to be monitoring Hangeland's situation at Craven Cottage with the big defender available on a free transfer next summer.
Fulham are keen to keep hold of the Norwegian international and Martin Jol is hopeful the 31-year-old will sign the lucrative new deal on the table.
"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," said Jol.
"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.
"You always hope people will be satisfied. We pay good wages and made him a very good offer.
"I didn't see him because I don't do the negotiations but the people who do that told me he was quite happy."
Jol added: "He's a nice lad if you know him. He's not an extrovert but down to earth."