On Friday, results from the initial wave of tests revealed that three people at the Bundesliga club had contracted the illness.
Midfielder Niklas Hauptmann, defender Ismail Jakobs and a physiotherapist were placed in quarantine and a second round of tests was carried out on Sunday on the other squad members.
They were all negative, the club said on Monday.
The German Football League (DFL) plans to resume play in the Bundesliga from 16 May behind closed doors.
The DFL says regular testing will be required and only players who have returned two successive negative tests will be allowed to train and play.
Government decision
On Sunday, Horst Seehofer, Germany's minister for sport and the interior, said he supported a resumption of the Bundesliga. The German government is expected to give its verdict on Wednesday.
When play was suspended on 13 March, Cologne lay in 10th place on 32 points with nine games remaining.
Bayern Munich led the 18 team division by four points. The Bavarians, who won the 2019 title, said all those tested had negative results.
If play were to resume in just under two weeks, the Bundesliga would be the first major European league to resume after a lockdown and would be a litmus for how action could resume in Spain or England.
Two weeks ago in the Netherlands, the Eredivise was declared null. No champions were assigned and there was no promotion or relegation.
Last week in France, the Ligue de Football Professionel attributed the 2020 Ligue 1 title to Paris Saint-Germain following the government’s decision to ban professional sports in the country where more than 24,000 people have died from the illness.
Though the death toll in Germany - at nearly 7,000 - is significantly lower than in neighbouring France and Italy, the German chancellor, Angela Merkel, has warned that the country should remain vigilant as lockdown measures are eased.
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