Published: 2020-08-10 20:16:21 BdST
The club's morning training session was postponed due to the positive cases and their plans to travel to Lisbon were put on hold, but the club said in a statement they would have one final session before flying out on Tuesday, a day later than planned.
The statement revealed that the two players to test positive were forward Angel Correa and injured defender Sime Vrsjalko, who will miss the trip and were isolating at home, adding that the pair were both asymptomatic.
Atletico, who are bidding to win the competition for the first time after falling in the 2014 and 2016 finals, face German side RB Leipzig on Thursday in the quarter-finals, hoping to set up a last-four meeting with Paris St Germain or Atalanta.
"The first team squad and coaching staff underwent COVID-19 tests on Sunday and they all came back negative, after two positive tests were registered following the previous tests on Saturday," said Atletico's statement.
"In keeping with health protocols, those who share a home with the two players who tested positive also received tests, which came back negative.
"The club's medical services have been authorised by the two players to reveal their identity in order to end speculation."
Atletico did not register any positive cases for the virus when La Liga re-started in June after a three-month hiatus due to the pandemic as the top-flight was successfully completed without any major incidents.
But mass positive tests at Madrid side Fuenlabrada last month threw the finale of the second division season into chaos, while cases across the country have continued to rise, with 1,895 new cases reported by the health ministry last Friday.