Barca announced on Thursday that Dembele must leave the club before the end of the month after failing to agree a new contract at Camp Nou, with just six months to run on his deal.
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Director of football Mateu Alemany said the Catalan club do not want players "who are not committed," with coach Xavi Hernandez dropping him from the squad for Thursday's Copa del Rey tie at Athletic Bilbao.
However, the AFE have advised Barca they could be breaking the law by cutting Dembele out of their plans and treating him differently to the rest of their players simply because he does not want to sign a new contract.
"A club is obliged to pay a player the agreed wages and allow the provision of services under the same conditions as the rest of his teammates, without there being any type of discrimination or pressure for the athlete to waive their working rights," the AFE said in a statement. "The renewal of a contract requires the agreement of both parties.
"Said agreement must be issued freely without any external conditions that limit the player's freedom. A footballer does not have the right to be called up for every match, but they must be treated under the same conditions as their teammates.
"If [Barca's actions] can be understood as pressure to break his will -- and if public statements are also made acknowledging this type of pressure -- we would be looking at illegal conduct.
"The AFE considers that not reaching an agreement to renew a contract does not imply a labour breach, so it cannot have any consequences. Not picking a player for a period of time without any injury, illness or physical impediment, supposes a devaluation of his image that will negatively affect his future contracts."
Thursday began with Barca announcing that Dembele would not travel to Bilbao with his teammates and Alemany telling the club's television channel that the France winger must find a new club before the end of January.
Alemany said that Dembele's camp had turned down several offers during six months of negotiations and that the club's understanding is that the player does not intend to sign new terms.
Later on Thursday, Dembele made it clear that he has no plans to move for now, saying in an Instagram post he would not "give in to any type of blackmail.
"I am 24 years old and like all men I have defects and imperfections," he said. "I've been through complicated moments, injuries, COVID has affected me.
"Without even one training session, the manager called on me [after recovering from COVID] and I responded... without complaining. I responded as I always have done because this is my PASSION. I am aware of how lucky to have the most beautiful job in the world.
"I forbid anyone from thinking that I am not implicated in the sporting project. I forbid anyone from attributing intentions to me which I have never had. I forbid anyone from speaking about me or my agent, who I completely trust.
"I am still under contract; I am completely implicated and at the disposition of the club and my coach. I have always given everything for my teammates and the fans... that won't change now."
Speaking earlier this week, Dembele's agent Moussa Sissoko had said that he would defend his client "however necessary" if Barca followed through on a threat to leave him in the stands until the end of the season in the event he chose to run his contract down.
Sissoko, speaking to RMC in France, acknowledged that he had made "certain demands" during the negotiation process but added that Barca had shown a reluctance to negotiate.
Barca coach Xavi has spoken of his desire to keep Dembele, saying he could be the best player in the world in his position, but he was the one who made the final decision on Thursday to leave Dembele out of the squad. Xavi has also said that Dembele told him several times he wants to stay.
A January exit would depend on the player, with sources at the club telling ESPN last year they believed his camp was happy to run down his contract before leaving for free. That way, they would obtain a higher signing on bonus and make more in commission.
Sources told ESPN that Barca would be willing to let him leave for "next to nothing" this month to get him off the wage bill and make room for new signings, with some reports suggesting they are even exploring ways to rescind his contract if necessary.
Dembele, who has been linked with a move to the Premier League, joined Barca from Borussia Dortmund as a replacement for Neymar in 2017. He has endured an injury-hit four years at the club, though, and has made just 129 appearances in that time, scoring 31 goals.