Both Washington and Asomugha are dedicated activists and philanthropists involved with the William J. Clinton Foundation.
E! said Asomugha's manager Mark Holden, of Zero Gravity Management, was not able to confirm or deny the relationship.
Washington's representative told the media outlet, "We don't comment on our client's personal life."
Washington is best known for her work in the TV show "Scandal," as well as in the films "Django Unchained" and "The Last King of Scotland."