The Kushner family appeared on Friday to have struck a deal to buy out its partner in the troubled Fifth Avenue skyscraper at the center of its real estate empire, according to a filing with the Securities and Exchange Commission.

The Kushners’ partner, the publicly traded Vornado Realty Trust, has indicated for months that it was interested in selling its stake in the building, and on Friday, Steven Roth, Vornado’s chairman, said in the filing that it had reached a handshake deal “to sell our interest to our partner.”

The Kushners have attracted enormous public attention because of their connection to President Trump. Jared Kushner, Mr. Trump’s son-in-law, was chief executive of the company until he joined the White House last year as one of Mr. Trump’s key advisers.

The Kushners have spent the last three years on a worldwide hunt for a new partner and financing to build either a new super-tower designed by the architect Zaha Hadid on the site of 666 Fifth Avenue, near Rockefeller Center, or to renovate and reposition the 41-story, aluminum-clad tower as a first-class building.