The American international is free to make a temporary return to England from the Seattle Sounders next month, with the MLS season now in its winter break.
Although the majority of the division’s stars will be taking a break to recover, Dempsey is keen to carry on playing in a bid to maintain his fitness ahead of the 2014 World Cup.
A number of Premier League sides are interested in luring the Texan back across the Atlantic Ocean, but Fulham are hopeful that they can tempt him to spend a second spell at Craven Cottage.
The versatile attacker made his name in Europe with the Cottagers, before switching to Tottenham last year.
His spell at White Hart Lane was a difficult one, which led to an eventual return to his homeland to sign for Seattle over the summer.
The likes of West Ham, Everton and Stoke have all been linked with Dempsey, but Fulham chief Rene Meulensteen is confident that he can re-sign the USA ace.