The Spanish side conducted pre-season tests on players not on international duty, but Costa and team-mate Santiago Arias were also excluded having already tested positive during their holidays.
Atletico said the duo were currently isolating and showing no symptoms. As a result, they will not be part of the group which return to training on Friday.
Our first team players underwent the pre-season tests on Thursday, except for those who are currently on international duty and Diego Costa and Arias, who tested positive during their holidays and are currently isolating.
— Atlético de Madrid (@atletienglish) September 3, 2020
Elsewhere, France goalkeeper Steve Mandanda will miss Les Bleus’ Nations League matches against Sweden and Croatia after testing positive for Covid-19.
“As per the UEFA rules, the entire French delegation underwent tests on Wednesday at Clairefontaine in view of the trip to Sweden for the Nations League match this Saturday,” the French Football Federation said in a statement.
“The test of Steve Mandanda was positive for coronavirus, the goalkeeper underwent a second test in the same day. This was also positive. Steve Mandanda cannot therefore take part in the match against Sweden and will leave the group on Friday.”
Three further Paris St Germain players have tested positive, taking the total number within the French champions’ squad to six.
PSG confirmed the news in a statement on Thursday evening.
The capital club have been given a delayed start to their Ligue 1 campaign because of their run to the Champions League final last month, and will begin their domestic campaign against Lens on September 10th.