The Miami Herald reports the announcement is expected to be made at a news conference Tuesday in New York.
Dolphins owner Stephen Ross gave Anthony and four of his children a tour of Land Shark Stadium last Tuesday, Blanca LaSalle, a spokeswoman for the singer, said. Ross and Anthony are friends.
NFL Commissioner Roger Goodell and George Bodenheimer, president of ESPN, are expected to join Anthony and Ross for the news conference.
The Oct. 12 contest between the Dolphins and the New York Jets in Miami has been designated the NFL Hispanic Heritage Game of the upcoming season. Anthony is expected to perform during the game, to be shown on ESPN.
Gloria and Emilio Estefan are already minority partners in the Dolphins.