Dembele's current deal at Camp Nou is due to expire next June, meaning that, as it stands, he will be free to discuss terms with foreign clubs at the start of 2022.
Barcelona boss Xavi is desperate for the France international to sign a new deal, but the World Cup winner is allegedly weighing up his options amid interest from Manchester United, Chelsea, Liverpool and Juventus.
According to Mundo Deportivo, Newcastle, boosted by their Saudi takeover, have offered Dembele a contract worth €15m (£12.6m) per season, in addition to the same amount as a signing-on bonus.
Barcelona are struggling to come to an agreement with the 24-year-old due to their financial problems, which is preventing them from being able to offer him a significant pay rise.
Dembele has only made two appearances at club level this season due to injury, but he is in line to make his first La Liga outing of the 2021-22 campaign against Villarreal on Saturday.