Dembele, 23, continued his fine start to the season on Wednesday with a goal and an assist in Barca's 3-0 Champions League win over Ferencvaros in Budapest.
A source at Barca told ESPN that the club are aware Manchester United are still monitoring the France international's situation but that the Blaugrana are confident of getting him to commit to a new long-term deal. Negotiations have been ongoing now for several weeks.
United tried to sign Dembele in the summer on loan with an option to buy at the end of the season. However, the player did not want to make the switch to Old Trafford, despite Barca's openness to letting him leave at the time, because he is desperate to succeed at Camp Nou.
Barca's transfer business is on hold until Jan. 24, when a new president will be elected. A managing committee has been overseeing the day-to-day running of the club since Josep Maria Bartomeu resigned in October.
Despite that, the sporting directorate, led by Ramon Planes, are pushing ahead with plans for the future with the aim of leaving the club in the best possible position when a president is chosen.
It will then be up to the incoming president to give the green light to any signings or contract extensions Planes and his team, who are working closely with coach Ronald Koeman, have put in place.
After returning from a seven-month injury layoff, Dembele has gradually earned his place in Koeman's side this season, contributing four goals and two assists in 11 appearances.
A dressing room source at Barca told ESPN that Dembele, who is in his fourth season at the club, "is doing everything asked of him and that's why Koeman's giving him so many minutes."
Barca also want to extend Dembele's contract to protect his value on the transfer market. Next summer he will move into the final 12 months of his deal and in 2022 he could potentially walk away for free.
Dembele's time at Barca has been severely hampered by fitness issues. He has suffered eight muscle injuries and had to be operated on twice.
He made just nine appearances last season in all competitions and has made 85 in total since moving to Camp Nou.