The 28-year-old did not reveal where he would be playing next but widespread reports in the Spanish media said he would be joining Barcelona.
Real Madrid win UEFA Champions League
Images from Europa League matches played across Europe on Thursday.
Atletico Madrid made sure of at least a third-placed finish in La Liga and secured a berth in the Champions League group stages for next season with a 3-1 win away to struggling Celta Vigo on Wednesday.
Real Madrid manager Carlo Ancelotti said on Saturday he is happy with how new signing Kylian Mbappe is settling into life with the Spanish soccer giants and he has no concerns about his team's slow start to the LaLiga season.
Diego Simeone may not have the stomach to reinvent Atletico Madrid again after they suffered another morale-shattering loss to Real Madrid in Saturday's Champions League final.
'I haven't always expressed myself well. I said I would like to play with Neymar and Mbappe, but that doesn't mean I want to go to PSG'
Atletico Madrid have been unable to repeat the magnificent achievements of last season in this campaign but can congratulate themselves on a job well done if they secure a lucrative Champions League berth on Saturday.
A round-up of Sunday's matches in LaLiga, Ligue 1 and Serie A
Atletico Madrid's fears of further disruption to their trip to the Champions League 'Final Eight' tournament in Lisbon have been eased after the rest of the squad tested negative for COVID-19, following two positives the previous day.
Atletico Madrid striker Antoine Griezmann struck twice as the Spanish side outclassed hapless Olympique de Marseille 3-0 on Wednesday to win the Europa League for the third time.
Costa has not played for Chelsea since the FA Cup final in May, following which he claims manager Antonio Conte sent him a text telling him he was not in his plans for the new season.
Barcelona closed to within a point of La Liga leaders Real Madrid when Lionel Messi scored one goal, created two and conceded a penalty in a 3-1 win at home to champions Atletico Madrid on Sunday that eased pressure on under-fire coach Luis Enrique.
The 21-year-old is the latest youngster to join Atletico who have also brought in Argentine forward Luciano Vietto from Villarreal since the end of last season.
Coach Diego Simeone goes home 'content' after his team's 1-0 loss in their Champions League match on Wednesday
Carlo Ancelotti's side were then reduced to 10 men in the 79th minute when Vinicius Jr was shown a straight red card for slapping Valencia goalkeeper Stole Dimitrievski.
Portugal midfielder Maniche and playmaker Deco have been ruled out of the next two World Cup Group One qualifiers in Sweden and Albania.
Juventus striker Carlos Tevez would be a perfect fit for Atletico Madrid and the La Liga club are in talks with the Argentine's agents, coach Diego Simeone has said.
Champions Barcelona reclaimed top spot in La Liga on Sunday by overcoming a dogged Villarreal side to win 2-0 at home with goals from stalwart defender Gerard Pique and youngster Carles Alena taking them above Sevilla.
Russian clubs ruled the Europa League roost on Thursday as Rubin Kazan upset holders Atletico Madrid while Anzhi Makhachkala and Zenit St Petersburg opened up commanding first-leg advantages in their last 32 ties.
Former player and reserve team boss Santiago Solari has been put in caretaker charge after negotiations between the club and former Chelsea, Italy and Juventus boss Antonio Conte broke down on Monday, the club added.
Atletico said they are collaborating with authorities to identify the abusers who would be banned by the club. The Prosecutor's Office of Madrid is also investigating the case.
Twelve of Europe's leading soccer clubs from England, Italy and Spain announced a breakaway league on Sunday but after 48 hours of massive pressure from fans, politicians and even British royals the six English clubs backed out
Sunderland manager Sam Allardyce reckons Atletico Madrid boss Diego Simeone would be labelled boring for his defence-oriented style if the Argentine were managing a Premier League club.
A subdued Fernando Torres helped Atletico Madrid to a 2-0 win over local rivals Real in the first leg of their King's Cup last-16 tie on Wednesday in his first start since his return to his boyhood club.
Both managers have struggled in the Champions League this season, with PSG on seven points and 25th in the standings, one place outside the knockout phase playoff zone, while City are one point ahead in 22nd.
Atletico Madrid surrendered top spot in La Liga to Barcelona when they were held to a 0-0 draw at home to 10-man Sevilla in a fiercely contested La Liga clash on Sunday.
The Spanish Football Federation (RFEF) and LaLiga have taken steps to tackle an increase in racist abuse with measures including partial stadium closures.
Zinedine Zidane has stepped down as Real Madrid coach with immediate effect five days after his team were pipped to the La Liga title by city rivals Atletico Madrid, the Spanish club said on Thursday.
France forward Griezmann, 28, rejected a move to Barcelona last year but announced in May he was leaving the Madrid side, where he has spent the last five seasons since signing from Real Sociedad in 2014.
Zlatan Ibrahimovic pulled up at the end of the session, possibly with a calf muscle problem. Atletico Madrid's record signing Joao Felix is likely to miss the start of the Spanish soccer season when it resumes next month after sustaining a sprained knee in training.
News of all that's transpired on and off the football field
Atletico Madrid's Argentina striker Sergio Aguero has been granted dual Spanish nationality, the La Liga side said on their website (www.clubatleticodemadrid.com) on Friday.
Towering goalkeeper Thibaut Courtois, who joined Chelsea from Belgian champions Racing Genk earlier this month, is to spend this season on loan at Atletico Madrid.
In the dying minutes of their Champions League semi-final second leg against Real Madrid, a thunderstorm rolled in and drenched Atletico Madrid's Vicente Calderon stadium.
A downbeat Diego Simeone did not confirm whether he wanted to continue as Atletico Madrid coach on Saturday after suffering a second agonising Champions League final defeat by Real Madrid in three years.
Joaquin, 37, became the oldest scorer in a Seville top-flight derby when he rose to head home at the near post in the 79th minute, shortly after the visitors had had midfielder Roque Mesa sent off for two bookings.
Real Madrid have sacked coach Carlo Ancelotti after the world's richest club by income failed to win major silverware this season.
Villarreal have agreed to sell Argentine forward Luciano Vietto to Atletico Madrid, president Fernando Roig has said.
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