The 24-year-old Belgian international midfielder has turned in a series of impressive performances for the Cottagers this season, and has attracted the attention from a host of rival Premier League clubs.
Gunners boss Arsene Wenger is known to be in the market for reinforcements at the end of the current campaign, and could turn to Dembele - a player who has developed into one of the most accomplished playmakers in England's top-flight.
However, Arsenal will face competition for his signature as Spurs boss Harry Redknapp is also keeping tabs on his situation, and will make a move to bring him to White Hart Lane when the transfer window reopens.
However, with his long-term Tottenham future shrouded in doubt, that could put pay to the clubs intentions of signing Dembele, who is rated at £15 million.
Fulham are keen to agree new terms with the former AZ Alkmaar midfielder, who moved to Craven Cottage from the Eredivisie for £5 million in the summer of 2010.
However, Martin Jol is well aware that he will not be able to compete with the likes of Tottenham and Arsenal in terms of wages or club status, particularly now that Liverpool have emerged as contenders.
Kenny Dalglish is also expected to be busy in the transfer market this summer, as he looks to take his Reds squad to the next level by bringing more players to Anfield.