Johnson’s current contract is set to expire next summer, but Jol is keen to keep the former England striker, who notched abrace against Odense in the Europa League.
Jol said: “He is top scorer in Europe if you count qualification matches too. He was a handful tonight.
“He hasn’t done it in the league but sometimes you have to give him the opportunities too.
“The second goal was unbelievable. The ball was high and he took it on his shoe. It was amazing. It came from nothing.
“We have offered him another two years so there is a lot of confidence in him.
“Sometimes it’s better to start talking in December or January. Andy is a good boy and a good worker.
“He has one year left and hopefully we can change that. If not, it is in his hands.
“He is a team player and will give you his all. He was good for us today and Fulham has been good to him before my time here.
“He has had a lot of big injuries and didn’t score a lot of goals last year, just two, maybe three. It’s a good marriage, you know?
“I want Andy to be with us and stay here. I don’t think there’s a lot of difference [in the negotiations].
“We have spoken a couple of times in the last couple of weeks.”
Jol has hinted that Johnson could start the Premier League clash with Queens Park Rangers on Sunday.
“I’m 100% certain that if I start Andy he won’t let anyone down,” the Dutchman added.
“He is a true professional, he always plays with his heart and you can’t say that of all the pros in football.
“We didn’t do particularly well in first half. We have to look at every game again. If we’d scored against West Brom there’s no problem. We have had five draws. It’s ridiculous.
“It means we are good defensively but we couldn’t put the ball in the net.”