The Premier League club were close to agreeing a move for the 19-year-old - who is out of contract in the summer (via London Evening Standard) - during the January transfer window, but the London Evening Standard reports that the Cottagers' desire to keep him until the end of the campaign as part of the deal meant that the move fell through.
And that appears to have allowed Benfica to enter the race. The Primeira Liga leaders had scouts in attendance at Fulham's game with Burnley on Tuesday, the London Evening Standard reports, and they would undoubtedly have been impressed by what they saw.
The Frenchman set up one for strike partner Ross McCormack before getting on the scoresheet himself. And while the Clarets would go on to win the game, Dembele's performance would have certainly left Benfica's representatives feeling optimistic about the youngster's potential.
His strike against the Championship leaders was his 12th league goal this season, and that form has been a key reason why, despite their lowly position in the table, only Tuesday's opponents have scored more than Slavisa Jokanovic's side this term.