The German lender has done business with the current U.S. president for decades, and there have been hundreds of millions of dollars' worth of loans made to Trump businesses through a Deutsche Bank unit, according to multiple reports.

But, speaking on the sidelines of the Singapore Summit, the CEO declined to comment on whether the bank has received a subpoena for the federal investigation into Trump and his campaign.

"I think we've agreed we wouldn't comment on that matter other than to say that if we do receive a request — potentially in the form of a subpoena, but there are other forms of formal request — by which we're bound, then of course we will cooperate fully with any official investigation," Cryan said.

"But we cannot just share with the public information about any client, whoever that client is, because it's ... illegal but it's also incredibly bad practice," he added. "So we will always follow the rules, we will always follow the law, but we can't just compromise our clients' confidential data."

Cryan declined to comment on whether Special Counsel Robert Mueller or anyone from his team had been in touch with the bank.