The possibility raised by the firm's chief regulatory officer was the latest warning from a financial firm since the UK voted to leave the European Union.
Currently, UK-based companies can conduct business throughout Europe, but could lose that right.
However, Deutsche Bank has said it is committed to the City of London.
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Sylvie Matherat, chief regulatory officer at Deutsche, made the remarks on Wednesday.
The positions in question include not just front office jobs, but also roles in IT and risk management, she said.
"For front office people, if you want to deal with an EU client, you need to be based in the EU," she said during a panel at the Frankfurt Main Finance Conference in Germany.
"Does it mean I have to move all the front office people to Germany or not? We're speaking of 2,000 people."
She added that an additional 2,000 jobs linked to risk management could also face relocation.
"So we really need clarity," Ms Matherat said. "We are the largest bank branch operating in the UK. We do have something like 9,000 people there, so I mean they [staff] do have real questions [including] where do I register my children for in the next two years at school? I mean that is a very concrete question."
Despite the warning, the bank last month entered negotiations for a new London headquarters with a 25-year lease.
Deutsche Bank is considering moving as many as 4,000 jobs out of the UK as a result of Brexit - nearly half the firm's current workforce.