Johnson, who is out of contract at Craven Cottage at the end of June, has battled injury problems during most of his time at the club.
And the former Everton forward's agent, Anthony McFarlane, suggested a move to the lucrative United Arab Emirates league could now be on the cards for his client.
"He is now 31, and he has never been in this situation in his career where he is available on a Bosman," McFarlane told UAE sports daily Sport360. "His mind is open and he's looking at all his options, both here in England and abroad. He is keen on a new challenge and very interested in a move to the UAE provided the offer is right."
McFarlane added: "He's married, he's got two kids and a move to the UAE would provide a nice lifestyle and a new experience for AJ and his family. There have been no concrete offers as such at this moment in time, but there has been strong interest from a number of clubs in the gulf area, including a couple from the UAE."
Meanwhile, 29-year-old Dempsey has again expressed his desire to play Champions League football as soon as possible. The United States international scored 17 Premier League goals last season and has been linked with a move to the likes of Arsenal and Manchester United.