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.