Labbadia has struggled to get a working relationship with the general manager at the club working and has been linked with the job as Hamburg coach.
“We have spoken with some of the people concerned on Monday and Tuesday and have singled out the points which need to be worked on,” general manager Wolfgang Holzhauser told Bild.
“The scales are finely balanced,” he told the Cologne Stadtanzeiger newspaper.
“Bruno Labbadia is and remains a very good coach. He works very meticulously, is very diligent and goes into detail with each player individually.
“He led us to the cup final, which is also worth something. But ninth place in the Bundesliga and the timing and style of some of his interviews go against him.”