The former Everton striker's current deal is due to expire in the summer, although talks are ongoing to extend his stay.
Question marks have been raised over Johnson's long-term future after manager Martin Jol revealed he shunned the club's initial offer.
Johnson proved his credentials over the weekend with a hat-trick in Fulham's 6-0 demolition job over newly-promoted QPR.
Dempsey is a big fan of Johnson's ability and hopes the striker stays with the London outfit.
"That's not for me to make that decision," Dempsey told the Fulham Chronicle.
"But AJ's a goal scorer and he's good to have around, and hopefully that will be the case for some time to come.
"He also likes to have a laugh and I respect him for the fact he's had some tough injuries and fought back from them."