John Cryan said Friday that the bank was not just thinking about competition with other financial institutions but other sectors like technology.
Speaking at a banking conference in Frankfurt, Germany, Cryan said: "Probably the most interesting thing, certainly the one on which we spend most time, would be: can we be competitive against companies that are not banks? Can we, for example, be competitive in payments versus companies that purport to make payments but are not regulated in the art of making payments?"
A number of so-called challenger banks — smaller institutions set up with the aim of disrupting larger lenders — have made significant headway in recent years, launching current accounts and seeking regulation among other things. One challenger, Revolut, said last week it had applied for a European banking license.
But Cryan raised concern about institutions that are not yet regulated. Facebook, for instance, lets users send and request money on its Messenger app via their PayPal accounts.
"Can we be competitive against technology companies in what is a world that is becoming more and more based on smart technology?" the bank executive said.
Deutsche Bank's boss also highlighted Starbucks as a firm that is accounting for a large part of the banks' business — deposits.
"Starbucks… takes a huge volume of deposits — it just doesn't look as though they're taking deposits because they're taking pre-payments," he said.
Starbucks customers are able to deposit money into accounts using the corporation's mobile app. Data from S&P Global Market Intelligence last year found that the business had more consumer cash in deposits than some banks.
This would not be the first warning that Cryan has issued over technology.
In September, he said that "a lot of people" in the banking industry will lose their jobs due to automation. This month, he went as far as to suggest that half of his bank's 97,000 employees could be replaced due to artificial intelligence and machines.