Federal prosecutors in New York are examining a $285 million loan that Deutsche Bank AG made one month before election day last year to the real-estate company run by the family of Jared Kushner, according to a person familiar with the matter.

Prosecutors from the Brooklyn U.S. attorney’s office issued a document request in mid-November to Kushner Cos., asking for contracts and other information pertaining to the loan from the bank, this person said.

Chris...