Ackermann resigned this week in the wake of the death of Chief Financial Officer Pierre Wauthier, 53, who was found dead in his home in Zug, Switzerland.
Ackermann, the former chief executive officer of Deutsche Bank, said he was resigning to avoid embarrassing the company. He said Wauthier's family would likely believe him to to be partly to blame for Wauthier's death although he also said he did not believe he was at fault.
The New York Times reported Friday the company said it would investigate to see if Wauthier had been under any undue pressure at work.
The company also said the incident had no bearing on the corporation's performance.
"I want to make it crystal clear that there is no link between this news and Zurich's business and financial results," Zurich Chief Executive Officer Martin Senn said Friday.
The Tages-Anzeiger, a Swiss newspaper, reported Wauthier left a note before taking his life that called attention to pressures he was facing at work.
The Times said Ackermann was known at Deutsche Bank for setting financial goals so high, some said they encouraged executives to take untenable risks.
While pledging to look into the matter, the company's executives were also focused on damage control.
"The recent developments have nothing to do with the quality of reporting or the accuracy of reporting," said Tom de Swann, who has taken over as interim chairman.
"There is no link in any respect to that," he said.