The two Atletico Madrid players who tested positive for coronavirus were Angel Correa and Sime Vrsaljko ahead of their Champions League quarter-final with RB Leipzig.
Both Correa and Vrsaljko are asymptomatic and are self-isolating at home.
All other members of the Atleti squad were tested again on Sunday and have returned negative results.
Atletico, who were due to fly to Portugal on Monday evening, will train in Spain before flying to Lisbon on Tuesday ahead of their match with RB Leipzig on Thursday.
Atletico said in a statement on Monday: "First team players and coaching staff underwent new PCR tests on Sunday and all results have come back negative. After two first team members tested positive on Saturday and following the health protocol, further exams were carried out on their relatives, all of which were negative.
"The club's medical services have been given permission to reveal their identities, thus putting an end to the speculation.
"The first team will return to training on Monday evening without Ángel Correa, who is asymptomatic and self-isolating at home, and Sime Vrsaljko, who was recovering from an injury and not training with the group. The Croatian is also asymptomatic and will remain at home by decision of the medical services, although his case is considered to be resolved by the health authorities, having generated antibodies (IgG) several months ago. The doctors will monitor both players as per the health protocol.
"The club and its medical services would like to thank the media for the respect shown to the privacy of these two players.
"As a result, 21 first team players and Academy footballers Álex Dos Santos, Manu Sánchez, Riquelme and Toni Moya will travel on Tuesday to the Portuguese capital to focus on the Champions League quarter-final."
The format of the final stages of the Champions League were amended following the coronavirus pandemic with the quarter-finals, semi-finals and final all now set to be held in Lisbon, Portugal.
The remaining matches are one-legged ties played in Lisbon at Benfica's Estadio da Luz or Sporting Lisbon's Estadio Jose Alvalade.
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