The 19-year-old marksman has been in excellent form of late for the Cottagers, notching five goals in his last five outings to take his total for the current season to eight in 18.
And this recent razor sharp run is understood to have alerted Spurs, with reports claiming that a move for the teenager is on their agenda.
Dembele dropped from the Premier League with the London side after the 2013/14 season and with his contract up at the end of the campaign Fulham may find it hard to keep him at Craven Cottage.
Even though he would technically be a free agent, the Championship side would be due a compensation fee given his age if they make him see out his agreement.
However, Fulham are likely to be able to negotiate a higher sum this winter given the youngster’s potential and form.
Dembele is the namesake of Spurs man Mousa Dembele.