Warren Buffett, chief executive officer of Berkshire Hathaway Inc., is looking into swapping his $1.1 billion stake in Graham Holdings, formerly the parent company of The Washington Post. (Jeff Kowalsky/Bloomberg)

Warren Buffett is looking into getting rid of his $1.1 billion stake in Graham Holdings, formerly the parent of The Washington Post, and ending four decades as a stable, major shareholder in the diversified family-owned company.

According to a Berkshire Hathaway filing with the Securities and Exchange Commission, Buffett would relinquish his 23.4 percent stake in Graham Holdings.

In exchange, Graham Holdings would spin off some portion of its assets — which include lucrative broadcast television and cable subsidiaries as well as the for-profit Kaplan education business — into a new unit that would be owned by Buffett’s Berkshire. Buffett would also receive cash and the relatively small number of Berkshire Hathaway shares, worth about $3 million, owned by Graham Holdings.

The deal is still under negotiation and might not be completed, according to the filing. The structuring of the deal would carry significant tax benefits for Buffett and Graham Holdings.

If an agreement is reached, it would be the latest major change for Donald E. Graham’s company. In August, Graham decided to sell The Washington Post newspaper to Amazon.com founder Jeffrey P. Bezos for $250 million. Now, with Buffett potentially exiting the stage as well, Graham could be saying goodbye to another hallmark of the former Post company.

After Buffett’s stock is eliminated from the outstanding shares of Graham Holdings, shareholders would be left with a larger share in a smaller company, and Buffett would own assets he prizes more than the entire array of the Graham holdings.

Buffett, who served on the company’s board for 37 years until 2011, was close friends with Graham’s mother, Katharine, who wrote in her memoir that from their first meeting she “instinctively trusted him.” And his close watch over the company helped assure, for instance, that the employees’ pension fund was vastly overfunded.

He also benefited financially. Buffett began buying shares in what was then The Washington Post Co. in 1973, paying only $11 million for the $1.1 billion stake he has today. In addition, he received dividends that last year alone came to $17 million, more than his initial investment.

The complicated structuring of the deal under discussion — a tax-free exchange of shares — would enable Buffett to avoid the 35 percent corporate tax on his stock and Graham Holdings to avoid tax on the increased value of the assets transferred, experts said. Because of the large gain in the value of Berkshire’s investment, Graham Holdings might be able to inject assets worth somewhat less than the $1.1 billion value of Buffett’s stake in the company.

It wouldn’t be the first time Buffett had engineered a tax-free share swap. In December, he swapped his stake in Phillips 66 for a division of the company that made lubricants used in transporting oil through pipelines. Earlier, in 2008, he exchanged his 16.3 percent stake in White Mountains Insurance Group for cash and one of the group’s subsidiaries.