The squad underwent COVID-19 testing on Wednesday morning at the La Liga club's training ground in Majadahonda ahead of a return to individual sessions this weekend.
Multiple reports in Spain stated that the results showed while 10 players have been exposed to the virus, Lodi is the only one who remains contagious.
The 22-year-old Brazil international will begin a quarantine period at home, while his nine teammates will begin training on Saturday as they have recovered sufficiently to no longer pose a threat of transmission.
Atletico Madrid are not commenting on the reports, citing player confidentiality.
Lodi is now asymptomatic having first complained of flu-like symptoms in March.
The Brazilian full-back will be subjected to further testing in the coming days and will be allowed to rejoin training after two negative results, 72 hours apart, as set out in a protocol agreed by La Liga and Spain's National Sports Council.
Atletico are due to begin training this weekend in the first phase of a four-week process that will see La Liga clubs move from individual work to small-group activities and finally full sessions.
The club's plan allows up to six players to train separately on each of their five training pitches at any one time during this initial stage, with no interaction and a minimum two-metre distance between them.
La Liga hopes to resume the 2019-20 season -- which has been suspended since March, with 11 rounds of games still to play -- in mid-June, and complete it this summer.