• Activist investment firm Starboard Value has built a stake in News Corp.
• The firm's CEO Jeffrey Smith told CNBC's David Faber on Tuesday that Starboard has been in discussion with News Corp.
• Starboard is making the case that News Corp. should separate its real estate assets from its news business.

Activist investment firm Starboard Value is pushing for change at News Corporation, in particular to see its real estate business separated from the rest of the company.

Starboard CEO Jeffrey Smith told CNBC's David Faber on Tuesday that the firm is building a position in News Corp. and has been in discussions with the company.

Smith said News Corp. should split out its real estate assets, including an interest in REA Group of Australia. News Corp. also owns the Dow Jones news business, which includes publications such as The Wall Street Journal and New York Post.

"Our belief is they're going to want to … separate the digital real estate assets to be able to highlight this beautiful business for what it's worth," Smith said on CNBC on Tuesday.

A News Corp. spokesperson said Tuesday that the company has "always maintained an active and engaged dialogue with our investors and are committed to driving shareholder value."

"We remain focused on executing our strategic plan, which has helped us set records in profitability over the past three years," the spokesperson said. "We are proud of our rapid digital transformation and bright prospects for long-term growth and value creation."

Reuters and The Wall Street Journal earlier reported on Starboard's stake in News Corp. The size of the stake has yet to be learned. The Murdoch family trust controls about 40% of the voting rights of both News Corp. and Fox Corp., making change difficult at either company.

"It's not great governance to have dual class," Smith said Tuesday. "There have been votes to declassify, it's something to consider as well. But there are easier paths to create a lot of value."

On Tuesday, Smith called out the valuation discrepancies between the news and real estate businesses. He noted that News Corp.'s "crown jewel" news division trades at four-times earnings before interest, taxes, depreciation and amortization, compared with competitor The New York Times, which trades at 15 times.

Meanwhile, News Corp.'s real estate assets trade at eight times, he said.

"It's a great business, a great asset, it's just too cheap," Smith said of News Corp.'s stock price. News Corp. shares were slightly down Tuesday at $21.85.

He added Tuesday that he believes the split of the businesses hasn't occurred already because the company was "a little insecure" about leaving the news division alone for a period of time.

Starboard's push for change at the company comes shortly after Rupert Murdoch said he would step down as chair of the board at both News Corp. and Fox News owner Fox Corp. Effective in November, Murdoch, 92, will become chair emeritus of each company while his son, Lachlan Murdoch, will become sole chair of News Corp. and continue as Fox Corp.'s executive chair and CEO.

Lachlan Murdoch made the initial investment in REA Group two decades ago, which Smith called an "amazing investment" on Tuesday.

More than a year ago, Rupert Murdoch had explored reuniting News Corp. and Fox Corp., a move that would have allowed leadership to be consolidated in the Murdoch media empire while also cutting costs. The businesses were split up in 2013.

The push to rejoin the businesses had come as the audience shrinks for both print media and cable TV — Fox Corp. owns cable TV networks including Fox News — as readers and viewers increasingly get their news and entertainment from online sources.

However, the proposed merger was called off in January. In a letter to the board, Murdoch said he was withdrawing the merger as he and his son "determined that a combination is not optimal for the shareholders" of either of the companies at the time.

Smith said Tuesday that there had not been discussions regarding another push for a proposed merger.

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