The White House is looking to bolster its communications efforts by bringing in new communications staff dedicated to dealing with the impeachment inquiry, CBS News confirms.

Senior White House adviser Jared Kushner, who is also President Trump's son-in-law, has been pushing these efforts for some time. Several administration sources told CBS News that Tony Sayegh, the former spokesman for Treasury Secretary Steve Mnuchin, is being pushed by Kushner to lead the team.

The staff shakeup was first reported by The New York Times. Sayegh did not respond to a request for comment from CBS News.

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There has been dissent and criticism in the White House ranks, and among Trump allies, over the communications efforts from the president during the impeachment inquiry. Senior administration officials and former senior White House officials have confided to CBS News that they believe the White House has been losing the communications battle over messaging to the Democrats during the impeachment inquiry.

The chatter about bringing in help to better manage communications hasn't escaped Mr. Trump, but as a general principle, it's not something he's likely to admit he needs, not publicly, anyway. As he left the White House Friday for South Carolina, he told reporters, "Here's the thing: I don't have teams. Everyone's talking about teams. I'm the team."

A Republican congressional aide told CBS News that the White House is providing its allies on Capitol Hill with talking points after major developments in the impeachment inquiry. These talking points are reactive, not proactive, and sent around inconsistently, rather than daily. At one point the White House accidentally sent its talking points to Democrats when the president's call with the Ukrainian president had been published.

Informal conversations between Hill Republicans and White House staff have been taking place, but the Republican aide was encouraged by reports that the White House planned to ramp up its communications efforts.

Jason Miller, who was Mr. Trump's campaign communications director, told CBS News, "The president is traditionally 'org chart-agnostic,' so he wants results and isn't concerned as much by where the efforts are being housed. He just wants to turn on the TV and see his allies defending him."

Mr. Trump is also going to want a person he's familiar with, whom he likes on TV — perhaps someone already working in the White House or someone who has worked in the building before, Miller told CBS News. He thinks Sayegh would be a good fit for the job. "He's a killer," Miller said.

There were several meetings at the White House this week led by Kushner, acting White House chief of staff Mick Mulvaney and White House counsel Pat Cipollone to specifically discuss improving the strategy for addressing the impeachment inquiry, according to White House officials.

Kushner was a strong proponent of Sayegh, a former Fox Business Network contributor, during the internal discussions over replacing press secretary after Sarah Huckabee Sanders left. Kushner had advocated for Sayegh, but the spokeswoman for the first lady, Stephanie Grisham, was instead chosen to be White House press secretary.

Grace Segers contributed to this report