The 25-year-old is in the final few days of his existing deal with the Blaugrana but has not yet agreed a contract extension.
Spanish journalist Javier Miguel has said that Xavi revealed to him that Barcelona won't make another offer for Dembele. The 42-year-old added that the France international either has to accept the deal or leave in the coming days.
"Dembele is one step away from dropping his pants and accepting the offer he has had since December and which he has systematically ignored/rejected. on Monday I call Xavi asking him to intercede with Laporta. the technician, of course: 'There will be no new offer; either you accept the one you have or goodbye.'"
The club tabled an offer in December last year that was rejected by the player's representatives.
Xavi wants the former Rennes man to remain at the Camp Nou (via Marca). However, failure to agree terms next week could see the France international depart for free.
Dembele joined Barcelona from Borussia Dortmund in 2017 to become the club's then-most expensive player in history, arriving for €105 million plus adds ons. He was projected to be Neymar's long-term heir but has failed to deliver, largely due to injuries.
So far, he has scored 32 goals and provided 34 assists in 149 games across competitions for the Blaugrana.
Barcelona's dire financial health means they might be unable to offfer Ousmane Dembele improved offer
After multiple injury-plagued seasons that have impacted his output, Ousmane Dembele finally delivered consistently last season.
He was unplayable on several occasions and played a key role in Barcelona's resurgence in the second half of the season. The former Dortmund man starred with 14 assists in the league, which was the highest in the division.
Xavi wants Dembele to remain at Camp Nou, something the fans also want, but that might not happen.
The Blaugrana's financial difficulties are well-documented after years of mismanagement by the previous regime.
The club have had to take several cost-cutting measures to stay afloat, which might prevent them from making an improved offer for Dembele. Chelsea have been strongly linked with a move for the Frenchman (per The Express).