The 24-year-old £10million-rated Belgian playmaker has attracted interest from a host of clubs this past season with the likes of United, Premier League champions Manchester City, Arsenal and Chelsea all thought to be vying for his signature in this transfer window.
Red Devils' chief Sir Alex Ferguson was said to be in the driving seat as he looks to sign a long-term midfield replacement for Paul Scholes, who recently agreed a new 12-month deal at the club after coming out of retirement in January.
And, while Cottagers boss Martin Jol is desperate to keep hold of Dembele, who joined the Londoners after helping AZ Alkmaar lift the Dutch title in 2009, he could be tempted to offload him as he is about to enter the final year of his contract and would be able to leave on a Bosman free transfer next year.
However, when quizzed about a potential switch to Old Trafford or any of the other Premier League big guns, Dembele was keeping his cards close to his chest.
Ahead of Belgium's friendly international against England on Saturday, he said: "I know that there is interest from bigger clubs from the Premier League, but for now it is Fulham.
"Manchester United? Sorry, but I cannot say more about that at this time."