The 30-year-old’s current contract is set to expire in the summer and the striker has long been linked with a move away from Fulham.
“I would like to keep him,” said Jol. “We have always looked close to agreeing a deal and hopefully we are closer than ever before.
“You will find in the next couple of weeks or months we will have the same with other players.
“There is a song in my head – ‘You Can’t Always Get What You Want’ by the Rolling Stones.
“Sometimes you have to negotiate to put yourself in a position where the player is happy and the club has to be financially sound.
“Sometimes you have to give in, sometimes the players have to give in and that is where the problem lies.
“We are doing everything we can to keep Andrew Johnson, but there will be three or four other players, too.
“We have to extend a few contracts now. We have to try and find a solution in the next couple of weeks.”