Rodriguez, 41, has been working as a Fox in-studio baseball analyst since retiring from the Yankees partway through last season.
The deal came after Rodriguez served as a fill-in panel member on ABC's "The View" last week.
According to the New York Post's Page Six, the taping went so well, ABC executives thought Rodriguez could be added to the network's news division.
Anonymous sources inside ABC said Rodriguez could appear on other news broadcasts, including "Nightline" and its flagship evening news program "Nightly News with David Muir" if the subject calls for it.
Rodriguez is still under contract with the Yankees, who are paying him his former player salary to serve as a team consultant after injuries and declining performance forced him into retirement.
Rodriguez has upped his celebrity profile of late after news he is dating singer/actress Jennifer Lopez.
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