ESPN says Barcelona have started conversations with Dembele over renewing his contract, which ends on June 30, 2022.
Sources close to the French forward, 23, have been speaking with the club.
Negotiations are beginning during a period that Dembele has played well in and he even wore the captain's armband against Ferencvaros.
Barca want to renew his deal to protect their investment. If not, he can walk away for free in a year and a half's time.