Clubs in the top two German divisions have returned 10 positive results from 1,724 coronavirus tests, says the German football league.
Clubs have been training in groups, with the tests taken before a planned return to training as teams.
Measures including "the isolation of the affected person" have been taken, said the DFL.
Top-flight side Cologne have had no further Covid-19 infections after three people tested positive last week.
The trio are "symptom-free" but remain in quarantine for 14 days, said the club.
The Bundesliga is set to become the first major football league in Europe to return to competition.
Officials suggested resuming on 9 May but the government delayed the decision and a restart may now be on 16 or 23 May.
Cologne said in a statement that "only players who have been tested negatively twice in succession are allowed to train and play".
The DFL added: "A second wave of tests will be carried out this week - here too there may be isolated positive test results, especially since one of the tasks of this second round is to reduce the likelihood of 'false negative' findings that can never be completely ruled out."
Last week, chancellor Angela Merkel said that any decision on if and when sports activities could resume would be taken on Wednesday, 6 May.
The league has been suspended since mid-March because of the global coronavirus pandemic.
The DFL has warned that many top-division teams will be in an "existence-threatening" financial position if play does not resume by June.