The trio - which reportedly consists of two players and a physio - were consequently told to undergo a 14-day quarantine procedure.
Cologne said Friday that three people had tested positive but didn't name them or say whether they were players, who are now training in small groups.
"Three people tested positive, all are symptom-free", the club statement said.
"I am surprised that players are allowing this", he said in reference to Cologne's training continuing with the rest of the squad instead of them all being quarantined as a precaution.
DFL chief executive Christian Seifert last week said the Bundesliga was ready to resume with matches behind closed doors in early May, with next Saturday touted as a potential date for the action to get back under way.
The league has been suspended since mid-March because of the global coronavirus pandemic. Clubs in England and Germany have already reopened their training centres, while the French league was cancelled last week.
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Most teams have not commented on test results. The DFL warned clubs in an email from director Ansgar Schwenken late Sunday not to share any more details of results with the media.
Cologne said they would not confirm any names out of respect for the privacy of the individuals involved.
The Belgian midfielder said the decision not to quarantine the whole squad "is a bit freakish", but he backtracked Sunday, when Cologne issued a statement to defend its measures.
"The appropriate measures, for example the isolation of the affected persons, were taken immediately by the respective clubs in accordance with the specifications of the local health authorities", it stated.
Testing will continue regardless of whether competitive games restart or not.
The cash-strapped clubs and league had been hoping for the green light to end the two-month suspension so the league can contractually finish by 30 June.
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