White House press secretary Sean Spicer is leading a search for his own replacement at the briefing room podium as part of a larger plan to shake up the White House communications operations, according to two people with knowledge of the effort.

Last week, Spicer and White House chief of staff Reince Priebus reached out to Fox News personality Laura Ingraham about the role of press secretary and Daily Mail editor David Martosko about the role of communications director, according to a White House official.

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Spicer and Priebus have had preliminary discussions with Ingraham and Martosko met with chief strategist Steve Bannon last week, according to the White House official.

Ingraham declined to comment. In a phone call, Martosko said “I can't hear you,” and then hung up. He did not respond to an e-mail inquiry.

FOX News host Kimberly Guilfoyle, who was considered for press secretary during the transition, is not interested in the position and has not been interviewed, according to the people familiar with the effort.

Deputy press secretary Sarah Huckabee Sanders, who has frequently filled in for Spicer, has told people that she doesn’t want the job of press secretary, according to a source close to her.

The White House has been seeking to restructure the press shop since communications director Michael Dubke resigned from the role last month.

“We have sought input from many people as we look to expand our communications operation,” Huckabee Sanders said. “As he did in the beginning, Sean Spicer is managing both the communications and press office.”

Spicer has been pushing to move into a new role senior to both the communications director and press secretary, according to the people familiar with the discussions.

“Spicer should be elevated and if he’s not, I would not blame him for leaving,” said the White House official. “The president owes him this much for all he’s done for him. Sean is indispensable and I think the president knows that.”

Trump and senior staff have expressed their displeasure with the way Spicer and Dubke handled the response in the hours following the firing of former FBI Director James Comey, according to two White House sources.

They were criticized for failing to line up surrogates to go on television and for not having talking points that call out the hypocrisy of Democrats, who criticized Comey when he was investigating Hillary Clinton.

Spicer, whose pugnacious style was lampooned on "Saturday Night Live" by Melissa McCarthy, has stepped back in recent weeks. He accompanied the president on his foreign trip to Saudi Arabia, Israel, and Europe in May, but wasn’t included among staffers who joined Trump at his meeting with the Pope—an oversight widely regarded as a slight for the devout Catholic.

Since Trump’s return, Spicer has shared the briefing podium with Sanders.

The Republican National Committee, under the leadership of Dubke and former White House deputy chief of staff Katie Walsh, managed the surrogate response when Comey testified two weeks ago before the Senate Intelligence Committee.

An adviser to Trump said the president hasn’t yet signed off on making changes to the communications shop.

“Until you have the president buying in, any outreach or talk, is just that,” this person said.