Special counsel Robert Mueller and federal prosecutors in New York are examining as much as $16 million in loans that a bank run by a former campaign adviser to President Donald Trump made to former campaign chairman Paul Manafort, according to court filings and a person familiar with the two investigations.

The investigation by Mr. Mueller’s team is centered on whether the loans from Federal Savings Bank, a small bank in Chicago run by chief executive Steve Calk, were made as part of a quid pro quo arrangement to secure Mr....