New York Gov. Andrew Cuomo's highest-ranking aide has agreed to meet with federal prosecutors this month as their investigation into the disbanding of an anticorruption commission intensifies, according to a person familiar with the matter.

Larry Schwartz, who holds the title of secretary to the governor, agreed in recent weeks to meet with prosecutors from the Manhattan U.S. attorney's office, the person said, a development that suggests investigators are interested in learning more about the administration's actions before...