Costa is widely expected to leave Stamford Bridge after his relationship with Antonio Conte broke down in January following a row over a potential move to Chinese Super League side Tianjin Quanjian.
"For me, it will be the most hard season of my career", said Conte, speaking ahead of Sunday's Community Shield match against Arsenal at Wembley.
"He was let go by Conte via text, without any explanation from Chelsea's leadership", Ricardo Cardoso, Costa's lawyer, told EFE. "For the club, for him and his agent and for me the situation is closed".
Chelsea spokesman Steve Atkins added: "The premise the lawyer has put forward is just wrong".
Chelsea have signed four players so far - defender Antonio Rudiger (Roma), midfielder Tiemoue Bakayoko (Monaco), striker Alvaro Morata (Real Madrid) and goalkeeper Willy Caballero (Manchester City) - but Conte wants more recruits.More news: Amit Shah to visit Odisha on three-day tour from Sep 6
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The lawyer repeated the claim that Conte had told Costa he was not wanted at Chelsea by text message in June.
Mendes has supposedly reminded Costa that he needs to find regular football this season or risk missing out on a place in the Spain team for the World Cup next summer - so sitting in the stands at Atletico for six months is not an option.
"The player knew the decision, his agent knew the decision, clearly the lawyer has not been well informed".
Former AC Milan goalkeeper Mario Ielpo has urged the Rossoneri to try and get their hands on Chelsea striker Diego Costa this summer. Conte repeated that Chelsea are lacking "in a numerical aspect", more than individual player quality or star power. This situation, according to Antonio Conte, was clear since January, but somehow we're now to the point where the lawyers are getting involved.
Costa, who has been exiled from Chelsea training, is keen to return to former club Atletico Madrid where he wouldn't be able to play until at least January.