Irenic's push comes after media mogul Rupert Murdoch's proposal last week to reunite his media empire by combining News Corp and Fox Corp, nearly a decade after the companies split.
The companies have formed special committees to evaluate the proposal. Irenic has sought a meeting with panel from News Corp, sources said, adding the investor would be prepared to oppose a deal if it undervalues the company.
News Corp did not immediately respond to a request for comment.
News Corp's media business is home to publications like the Wall Street Journal and the New York Post and book publisher HarperCollins.
Its digital real estate business made about $1.7 billion in revenue last year, which is 16.7% of its total $10.4 billion annual revenue. It is anchored by REA Group, in which News Corp has a 61.4% stake, which is worth about $5.8 billion.
News Corp shares were up 5.4% before the bell, while Fox fell 5.6%. The New York Times first reported the news on Sunday.
(Reporting by Svea Herbst-Bayliss in New York and Eva Mathews in Bengaluru; Editing by Arun Koyyur)