The USA international moved to Craven Cottage in January 2006 and has since become a key figure at the club, consistently making over 40 appearances for the last four seasons.
Arsenal are looking at the winger to fill a midfield void that was left vacant by the summer departures of Cesc Fabregas and Samir Nasri.
The North London outfit signed Mikel Arteta and Yossi Benayoun in deadline day deals in the hopes that the pair would make up for the lost creativity in the Gunners midfield.
However, there still appears to be something lacking at the Emirates Stadium and the side are being associated with moves for several attacking playmakers to help add to Robin van Persie’s magnificent scoring record, with Dempsey now a part of that shortlist.
The 28 year-old has made over 200 appearances for the Cottagers and is a firm fan favourite with the West Londoners, known for his ability to get the side out of a pinch.
The tenacious midfielder has also developed a reputation for his versatility and ability to operate either out wide or in a more central role.
Dempsey has scored 49 goals during his time at Fulham, coming up in crucial moments in the Europa League as well as domestic competition, gaining an experience that would prove as valuable to Arsene Wenger as his superb dribbling skills.
Although Arsenal fans will surely be hoping for a bigger name to relight their hopes of gaining a Champions League place, however Clint Dempsey would bring a proven Premier League attacker to the Emirates Stadium that could shine on the bigger stage.
The US veteran will also prove the more economical option compared to other transfer rumours, and Martin Jol may let his playmaker go if the Stan Kroenke funded Gunners can meet his £10m valuation.