The Washington Post was first to report the interview.
Dusty Baker was fired by the Nationals on Friday after two seasons. Baker won the National League East division titles both of his seasons, but then lost in the NLDS both times.
The Nationals are seeking their sixth manager since 2009.
Martinez, 53, played 16 seasons with nine teams in the majors as an outfielder and first baseman. He has been the bench coach with Joe Maddon since the 2008 season, first with the Tampa Bay Rays and then with the Cubs, since 2015.
Martinez has interviewed for managerial positions before and was a candidate for the Nationals job in 2013.