The Belgian international has been one of the finer points in Martin Jol’s side this season following the side’s disappointing start to the campaign.
The 24 year-old plays in a similarly tenacious style as Suarez and could complete the transfer for as much as £9m.
Dembele was already being linked with a move to Anfield over recent months, and it appears that the Uruguayan’s racism-based ban could encourage the Merseysider’s to make the move that much sooner.
Although Fulham deploy the Belgian in a winger role, Dembele has shown on more than one occasion that he is capable of functioning up top in a striking role as well.
Ajax attacker Christian Eriksen and Lille sensation Eden Hazard are two other names being mentioned with a move to the Premier League outfit however the Fulham asset, while not of the same calibre, would prove the most financially viable option for a signing that is primarily a short-term replacement.
Since his 2010 switch from AZ Alkmaar, Dembele has notched up over 40 appearances for the Cottagers, scoring six goals in the process.
Although the Kopites signed over £50m worth of midfield ammunition over the summer, Jordan Henderson, Charlie Adam and Stewart Downing haven’t yet performed to the levels that may have been expected of them.
This, combined with the long-term injury to Lucas Leiva as well as the Suarez suspension could perk the Reds into January action, with a move for the Fulham man said to be likely.