The 24-year-old only signed a contract extension with the Hoops last summer but their relegation to the Championship has seen him edge towards a move to their West London rivals.
"I like his creativity and, of course, sometimes it comes off when he scores a lot of goals and I think he was involved in 40 goals [during the 2010-11 Championship promotion season],” said Fulham manager Martin Jol.
"It is like Dimitar Berbatov - sometimes these fantastic talents will be blamed but I hope to find a way to gel him in together with the boys we've got.
"I think he can do a hell of a job for us because he is a tremendous player on the ball."
The Moroccan spearheaded QPR’s return to the top flight in 2010-11 with 19 goals but struggled to find the net over the next two seasons in the Premier League.
Jol was responsible for bringing Taarabt to England with Tottenham after signing him from Lens in 2007.
"Remember the fact he was an over £10 million player 12 months ago, so I think you have to take them when they are bad and hopefully he will show his potential here,” he said.