Published: 2022-01-20 23:48:30 BdST
Dembele, who joined Barcelona from Borussia Dortmund in 2017, has failed to deliver on his potential that made the Spanish club pay 105 million euros ($119.11 million) for his services, scoring only 31 goals in 129 appearances.
Barcelona, who have debts of more than 1.35 billion euros, risk losing him for free at the end of the season if he does not renew his contract and coach Xavi Hernandez has also said they will look to move him on if that is the case.
Alemany said the club has already told Dembele he "needs to leave immediately".
"The reality is that we began negotiations with his agents five months ago. During this time there has been continuous communication in which the club's position has been to want him to continue," Alemany told Barca TV.
"Different offers have been made to him, we worked really hard and put a lot of effort, we have done enough for the player to consider what he has to do with his future.
"We are 11 days away from the closing of the transfer window and we understand that... the player has decided not to continue and what we want are players committed to Barca. Both for his sake and for the club he has to leave as soon as possible."
Dembele said on his Instagram account that he "would not respond to any type of blackmail" from the club.
However, he did not elaborate if he would leave the club during the January transfer window.
"It's been four consecutive years that I have been listening things about me and I was quiet. But for now on, it's over," Dembele wrote.
"I forbid anyone to give the impression that I am not involved in the sports project or attribute intentions to me that I have never had. We are negotiating and I'll leave my agent with it."
The French winger was brought in as a replacement for Neymar who moved to Paris St Germain in 2017 in a record-breaking transfer when the French club triggered his 222 million euros release clause.
Barca also signed Philippe Coutinho using the funds from the Neymar deal but the Brazilian midfielder struggled to make an impact, spending the 2019-20 season on loan at Bayern Munich and joining Aston Villa on loan earlier this month.