Tottenham Hotspur continue to be linked with the £6million-rated player.
Spurs are on the look-out for additional fire-power and 19-year-old Dembele certainly fits the bill, and with his current contract expiring in the summer Fulham may well cash in on him this month to ensure they can generate a healthy sum from his transfer.
The Standard claims Fulham want around £6million for the player if he moves on during the current transfer window and if he lives up to his considerable potential that could prove to be a bargain.
However, while Tottenham manager Mauricio Pochettino may be looking at a player to act as additional back-up to first-choice forward Harry Kane now, Fulham would allegedly not allow that, with the French teenager instead seeing out the current campaign at Craven Cottage.
Dembele has played 28 times for the Cottagers this season, scoring 11 goals in the process, and he is developing a reputation as one of the most exciting young forwards in the country.
Whether he completes a move to Tottenham this month could now be down to whether Pochettino wants an instant fix or is prepared to wait until next season to start working with the player.