The Frenchman, who has missed the beginning of the new term through injury, sees his current deal at the Camp Nou expire in the summer, allowing him to discuss a pre-contract agreement with other clubs in January.
However, the Catalan giants are said to be keen to keep the forward at the club and see him as a major part of their plans, with club president Joan Laporta reportedly already in talks with the 24-year-old's agent.
According to Sport, the Blaugrana have planned a two-year extension with a previously-agreed pay cut, given the club's financial troubles, while also offering the alternative of a three-year deal on further reduced wages.
Having already attracted interest from the likes of Manchester United, who could look to swoop after the turn of the year, Dembele is yet to commit his future to Barcelona.
Since his £120m move from Borussia Dortmund in 2017, the Frenchman has made 118 appearances for the Blaugrana, hitting 30 goals and providing 21 assists, while adding two La Liga titles and two Copa del Rey trophies to his cabinet.