The request is part of an investigation by special counsel Robert Mueller into Russian interference in the 2016 presidential election that brought Trump to office, the paper said.
Flynn has pleaded guilty in a deal under which he agreed to cooperate with Mueller's investigation.
Earlier this week, two sources said that Germany's biggest bank had been subpoenaed for records.
A source close to the matter told AFP that the bank had received a subpoena from Mueller's team for documents related to its dealings with the US president and had already begun to provide them.
A second source familiar with the investigation told AFP that the subpoena was linked to Trump's indicted former campaign chairman Paul Manafort.
But the White House denied that the president was directly targeted.