The Norwegian centre-back comes out of contract at the end of the season but he and the London club have not been able to meet in their negotiations with a final offer now on the table.
Jol is unaware where speculation regarding some of his other players comes from but was open about Hangeland's situation at Craven Cottage.
"Our culture is that we always like to keep the players we want to keep," said Jol ahead of Saturday's away clash with Reading. "I don't know where the story that our star players are going is coming from.
"We always want to improve and don't tell anybody else, but I believe that's what we did in the transfer window. With (Mousa) Dembele it was different, he left three days before the transfer window closed after promising he'd stay.
"We spoke to Clint (Dempsey) 18 months before his contract expired, but he wanted to go to a Champions League club.
"So believe me, there isn't a situation where a lot of my best players would go. (Dimitar) Berbatov has two years, (Mladen) Petric one year and an option, so that is fine and (Hugo) Rodallega was a free transfer. (Sascha) Riether has an option.
"Brede is the only problem, but we've been talking to him for the last five or six months. But we've made him a good offer so if he wants to stay that would be fantastic."