Gunners boss Arsene Wenger is on the look out for attacking reinforcements in what is expected to be a summer of upheaval at the Emirates Stadium with the Frenchman keen to add fresh faces to his squad.
Dempsey is one of the players at the top of his list and Wenger is keen to steal a march on Premier League rivals Liverpool who have also been courting him this season.
His contract expires at the end of the next campaign and despite Fulham offering him a new three-year deal to remain on the Thames it’s rumoured that they will cash in if he fails to sign the extension.
The 29-year-old has enjoyed arguably his best season for the Cottagers since arriving from MLS side New England Revolution in January 2007 scoring 23-goals whilst playing in an out-and-out strikers position.
Despite his prolific form it’s thought Wenger wants him to play in a creative role behind captain Robin Van Persie and new recruit Lukas Podolski in a devastating attacking triumvirate.
To make that a reality he’ll have to fend off interest from Reds chief Kenny Dalglish who is desperate to bolster his front line after a disappointing first year back in charge on Merseyside.
Desmpsey was linked with a move to Anfield last week after chairman Tom Werner officially stated their interest claiming any club would be lucky to have the American in their possession.
That angered Fulham manager Martin Jol who claims Werner is effectively trying to tap-up his prized asset.
He said: “If a manager does that it’s different as it’s a tap-up. If it’s an owner, he probably does not know the rules.”