The club has begun negotiations with Dembele to extend the winger's terms beyond 2022, according to a report from ESPN UK's Sam Marsden and Moises Llorens.
The 23-year-old was reportedly among a slew of Blaugrana first-team players on the chopping block this past summer as part of a squad overhaul following the club's first trophy-less campaign in over a decade.
That alerted Manchester United, who viewed Dembele as an alternative to Borussia Dortmund's Jadon Sancho, whose move to Old Trafford famously collapsed during the summer window.
Reports suggest Dembele was content to stay in the Catalan capital and fight for his place on Ronald Koeman's team following a seven-month injury layoff. Dembele has repaid his manager's faith, recording four goals and two assists over 11 matches across all competitions this season.
Dembele is "doing everything asked of him and that's why Koeman's giving him so many minutes," a source close to the team told ESPN.
With Dembele's current terms set to expire in 2022, Barcelona hope a new contract for the speedy winger will also help protect any future value. Dembele joined Barcelona in 2017 from Dortmund for a €105-million transfer fee as a replacement for Paris Saint-Germain-bound Neymar.