The former Borussia Dortmund man has been plagued with injuries since his big-money move to the Catalan giants, but Dembele has enjoyed a fruitful start to the new campaign, particularly in the Champions League.
The 23-year-old already boasts three goals and two assists in Europe's premier competition this season, with Dembele scoring one and setting up another in Barca's 3-0 win at Ferencvaros in midweek.
However, with Manchester United reportedly waiting to swoop for Dembele, who will see his deal at Camp Nou expire in 2022, ESPN claims that Barcelona are determined to tie the France international down to a new deal as a matter of urgency.
The report says that the Blaugrana hierarchy are optimistic about the situation, but the club will need the approval of Barca's new president - set to be elected on January 24 - before signing off on any incomings or new deals in Catalonia.
Dembele has become a regular under Ronald Koeman this season and is understood to have the Dutchman's full faith after applying himself well in training, with a summer move to Man United supposedly falling through due to Dembele's desire to leave a legacy at Camp Nou.