A television show featuring Michael Avenatti, the lawyer who is suing President Trump on behalf of a pornographic film actress, and the former White House communications director Anthony Scaramucci was pitched to two cable networks in recent weeks, people briefed on the matter said on Thursday.

The prominent television agent Jay Sures discussed with executives at CNN and MSNBC the concept of a program where the two men would square off, according to three people briefed on the issue. Both have become frequent cable network guests — Mr. Avenatti as one of Mr. Trump’s greatest antagonists, and Mr. Scaramucci as a loyalist to the president even after flaming out after less than two weeks at the White House.

Representatives for MSNBC and CNN declined to comment, as did Mr. Sures and Mr. Scaramucci.

“I have no interest in television right now,” Mr. Avenatti said. “I enjoy my law practice and look forward to prevailing on behalf of my client Stormy Daniels,” he added, using the stage name of the actress, Stephanie Clifford. He did not respond to a question about why Mr. Sures made such a pitch involving him.

Mr. Avenatti has appeared on both CNN and MSNBC repeatedly in recent weeks, often several times a day on both networks. The appearances are one part of an aggressive public relations campaign he has waged on behalf of Ms. Clifford, earning him criticism that he is leveraging his position to both undermine Mr. Trump and promote himself.