The Catalans have been in discussion with the winger for months about an extension to his deal, which expires at the end of the season.
Dembele has struggled badly with injury troubles since his move from Borussia Dortmund in 2017 for an initial €105million, which have hampered his attempts to establish himself as a key player at Camp Nou.
Xavi, though, has been eager to see the France international stay at the club despite him playing just six times in LaLiga this season and in only 52 per cent of all Barca's league games since his arrival.
This week, Dembele's agent Moussa Sissoko told RMC Sport that he would not bow to "pressure" from Barca over his client's future and accused the club of making "threats of no longer playing in the side" rather than engaging in productive talks.
It appears Xavi and Barca's directors have had enough of the situation and the message to Dembele is clear.
"What I can say is that we are making a difficult decision. If he does not renew, the club has decided they will make a decision," Xavi told reporters ahead of Thursday's Copa del Rey clash with Athletic Bilbao.
"We've waited a long time. We have been in talks with him for five months.
"Either he renews or we look for an exit. In the end, the club has decided that if he does not renew, a solution must be found.
"We have to do what is best for the club. [Sporting director] Mateu Alemany has been talking with him and his representatives for months.
"It's not a pleasant situation for anyone, but what's clear is that the interests of the club must prevail here.
"He told me he wants to stay. It's a question for him. I've been really clear; I can't be more concise. Either he renews, or we look for an exit. It's all or nothing."
Xavi also made it clear he considers it a priority to extend the contract of defender Ronald Araujo, which expires at the end of next season.
"His renewal is a priority. He's a really important piece. He has a winning character," Xavi said.
"I hope an agreement is reached because he's a player for the present and the future. Ronald is a boy who adds a lot."