Bill Shine, a former co-president of Fox News and top lieutenant to the network’s founder, Roger Ailes, has spoken with White House officials about taking a position on President Trump’s communications team, according to several people briefed on the discussions.

Mr. Shine’s job prospects are unclear now that Mr. Trump has fired his communications director, Anthony Scaramucci, who also attended last week’s dinner</a> and worked with Mr. Shine during his tenure as a host on Fox News and the Fox Business Network. Mr. Shine’s association with Mr. Scaramucci may hinder his chances with some factions in the West Wing.

Mr. Scaramucci, during a profanity-laced interview with The New Yorker last week, seemed to signal that he was considering Mr. Shine for a position, suggesting that Reince Priebus, the now-ousted chief of staff, would attempt to capsize the appointment.

“‘Oh, Bill Shine is coming in,’” Mr. Scaramucci told the reporter Ryan Lizza, apparently in an impersonation of Mr. Priebus. He added, in colorful language, that Mr. Priebus would likely try to leak it.

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