The 16-year-old is recognised as one of the most highly-rated players in European football.
That is seen by the level of clubs interested in the attacker.
Borussia Dortmund, Juventus and Paris Saint-Germain want the teenager, as do a number of Premier League clubs, including Arsenal.
The Gunners, according to The Sun, could look to jump to the front of the queue with boss Unai Emery undergoing a rebuild of the club with youthful talent.
Yet, Dembele, who made his first-team debut on the final day of last season against Hearts, is contracted until 2021.
The London-star is yet to decide his international future having played for both England and Scotland at youth levels.