Mr. Levin, according to two people with direct knowledge of the visit, broached the possibility of Mr. Trump sitting for another interview on his new Fox News series, “Objectified,” a spinoff from last fall’s special. The show, which is expected to make its debut in September, is to feature interviews with celebrities who describe cherished objects in their lives.

One of Mr. Levin’s ideal guests is Tom Brady, the New England Patriots quarterback and a friend of Mr. Trump, and Mr. Levin planned to ask the president if he would help secure the athlete’s participation, according to one of the people who described the visit.

Mr. Levin, 66, visited the day after Mr. Trump’s first formal address to Congress, and was given a warm White House welcome. He received a tour of the presidential residence, including a stop in the Lincoln Bedroom — photographs of which he proudly showed to friends after returning to Los Angeles, one of the people said. Both spoke on condition of anonymity to share details of conversations that were intended to be private.

Repeated inquiries to Mr. Levin and TMZ brought no response.

Mr. Levin, whose White House visit was first described on Tuesday by the website Entitymag.com, is a lawyer who gained prominence as a commentator on the O.J. Simpson trial. He founded TMZ in 2005, building the Hollywood-focused operation into a powerful force in tabloid news, known for its scoops and its guerrilla interviews with celebrities at airports and other public places.

His interview with Mr. Trump, filmed in September, was a Barbara Walters-style, soft-toned profile of the Republican presidential nominee, who reminisced at length about his childhood in Queens, military academy education, reality television career and rise to prominence.