Cologne said Friday that three people had tested positive but didn't name them or say whether they were players, who are currently training in small groups.
"The experts evaluate it as such that, due to the hygiene and infection prevention measures in group training, we can continue to train with those who tested negatively as we had been," team doctor Paul Klein said on the club website Saturday.
Klein added no-one at the club was considered "category one" in respect of the three individuals who gave samples Thursday. That is typically someone who either lives with an infected person or had close contact with them.
Cologne's announcement brought criticism from Karl Lauterbach, a lawmaker with the Social Democratic Party, the junior partner in Angela Merkel's coalition government.
Lauterbach said on Twitter that "probably two players, one staffer" were infected. He is a professor of health economics and was based at Cologne University before entering politics.
"I am surprised that players allow this to be done to them. Football should be a role model, not 'bread and circuses,'" he wrote in reference to training sessions.
Players and staff around the league began giving samples Thursday as part of an ongoing process designed to enable teams to return initially to full training, then to games later this month.
Most teams have not commented on test results. Werder Bremen said samples given Thursday by its players and staff were all negative, and that they will undergo another round of testing Sunday. One player from another Bundesliga club, Paderborn, tested positive in March. (AP) AHAH