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According to Xavi, there is "no alternative" for the French forward, who has entered the final six months of his contract at Camp Nou.
Dembele has struggled since joining from Borussia Dortmund in 2017 for an initial €105million, and this month's transfer window could be a final chance for the club to recoup some of that outlay.
Barcelona director of football Mateu Alemany told Dembele this week he must leave "immediately", which prompted the 24 year-old to issue an angry riposte on social media.
"I am not a man who cheats and even less a man who has a habit of giving in to blackmail," Dembele wrote.
Barcelona is fed up and wants a resolution one way or the other, with Xavi seemingly willing to keep Dembele and let this storm pass if he agrees to extend his contract before the end of the month.
"Ousmane's situation hasn't changed," Xavi said. "He has to decide. He is training well, but he knows his situation perfectly. There is no more debate, I think I was clear. It depends on him now. There are still days left and there is no alternative."
The situation is one that Barcelona could do without as it reels from a Copa del Rey exit at Athletic Club's hands, and the crushing blow of losing teenage forward Ansu Fati yet again to a hamstring injury.
Fati could be out of action for months after the substitute was substituted during the Athletic game, seemingly in tears as he left the pitch.
Xavi said the plan, agreed with club doctor Ricard Pruna, was for Fati to play for half an hour, so when the cup game went to extra time it conflicted with Barca's intentions.
Fati, who entered the game just after the hour mark, came off injured in the 96th minute, an apparent recurrence of the problem that had recently kept him out for two months.
"Ansu is very affected," Xavi said.
A meeting will take place to decide on the next course of action, with Barca reportedly keen for Fati to go down the route of surgery.
"It is a relapse," Xavi said. "Pruna told me that he was to play for half an hour and extra time disrupted our plans. We are going to make a specific plan for him. On Monday we will have a meeting to decide what to do.
"I'm not a doctor, but we have to mentally allow him to recover. [We need to] let him forget about the injuries and make a specific plan. We have lost an impressive footballer and it affects us all, but he is the main victim. We must do an exhaustive follow-up so that he does not injure himself more.
"It's a shame. We are sad because we have tried to take good care of him and he has been injured again. This is part of football. We are suffering major setbacks and this is very serious."
Fati previously spent 10 months on the sidelines due to a serious knee injury, resuming his Barcelona career in September this season.
Despite his limited action, Fati is Barcelona's second-highest scorer in 2021-2022 with five goals. They have come in just 456 minutes of on-pitch action.
On Monday (AEDT) Barca travels to face Deportivo Alaves in LaLiga, with Fati definitively ruled out and Dembele also expected to be sidelined by the club.
Alaves has not won any of its last 10 LaLiga games against Barcelona (D2 L8), conceding 3.1 goals on average in these matches.
Barcelona has avoided defeat in its last seven away LaLiga games against Alaves (W4 D3), keeping a clean sheet in six of them. This is the Blaugrana's longest unbeaten run at Mendizorrotza in the top flight, but this season's Barcelona is a different proposition, with the loss of Lionel Messi and to a lesser extent Antoine Griezmann meaning it lacks presence on the road.
Indeed, Barcelona has won only two of its last 10 away games in LaLiga (D6 L2), beating Villarreal in November and Mallorca earlier this month. That follows a run of 12 wins from its previous 14 away games in the competition (D1 L1).
The likes of Sergio Busquets have come in for flak from supporters of the club, and Xavi says the veteran members of the team must justify their selection.
"The shots go towards the sacred cows, and they have to understand it," Xavi said. "The commitment of the veterans is spectacular, unquestionable, but now it depends on the performance. Until recently we didn't have many alternatives."
The former Al Sadd coach said he remains "optimistic" about Barcelona's prospects, and said there could be additions to his squad before the transfer window closes at the end of the month.
"We are working on it, in several areas," he said.