"I'll have to get back to you on that," said Deputy Press Secretary Lindsay Walters when asked on Air Force One if Trump now had his ideal Cabinet.

White House officials are apprehensive about Hicks' departure, given her unrivalled position in the President's orbit. Despite her title as communications director, Hicks was more accurately described by White House officials as Trump's right-hand-woman and media gatekeeper, providing needed doses of affirmation to the President and able to deliver bad news to him with few repercussions.

The internal jockeying to replace her - if Trump even chooses to do so - has featured backstabbing and planted news stories that, in turn, bash the leading candidates: Mercedes Schlapp, the White House strategic communications director, and Tony Sayegh, assistant secretary for public affairs at the Treasury Department.

Many close to the White House, however, expect senior adviser Kellyanne Conway or Press Secretary Sarah Huckabee Sanders to assume the role, at least temporarily. Sanders has grown close to the President since taking over the press secretary's job after the resignation of Sean Spicer last summer - and has been spending more time in the Oval Office lately.

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The job of communications director - which involves developing and executing the administration's long-term messaging strategy - has never been a particularly important one to Trump. Aides joke he is his own communications director, who upends carefully laid plans with a tweet or digression.

Trump, never disciplined, has taken to freelancing more of late, as he moves to surround himself with aides less likely to try to rein him in. A speech outside Cleveland on Thursday meant to be about infrastructure instead, as many of his events, felt like a campaign rally. And he has broken free of more of the restraints placed upon him by Chief of Staff John Kelly.

Trump hired John Bolton as national security adviser last week over Kelly's objections and didn't include his chief of staff in the Oval Office meeting in which the job offer was extended. And Kelly, who frequently listens in on the President's calls, was not on the call Trump made from the White House residence earlier this month during which, over staff objections, he congratulated Russian President Vladimir Putin on his re-election.

Though Kelly's job did not appear to be in danger, Trump has mused to outside allies of late about setting a West Wing structure with no chief of staff, reminiscent of his Trump Tower operation.

Aides said controversies around Trump's staff need to hit a certain decibel level to get the president's attention.

In the case of Shulkin, who was found to have inappropriately accepted gifts and travel, his parting came as he was under fire from all corners, including GOP- leaning veterans groups and good-government watchdogs. And Trump himself vented to confidants that the questions surrounding Shulkin undermined his campaign promise to help veterans, according to three White House officials and outside advisers who spoke on condition of anonymity to discuss personnel matters.

Officials said ethical questions swirling around other Cabinet members are not attracting the attention of the president in the same manner but caution that could change quickly.

Housing and Urban Development Secretary Ben Carson came under scrutiny after reports his agency was spending $US31,000 ($40,000) for a new dining set. Environmental Protection Agency Administrator Scott Pruitt has faced questions about $US25,000 spent on a soundproof "privacy booth" inside his office to prevent eavesdropping on his phone calls and another $US9,000 on biometric locks.

White House ethics officials, directed by Kelly, have warned Carson, Pruitt and others that further negative attention could change the dynamic and send them packing. But another Cabinet member, Attorney-General Jeff Sessions, may have inadvertently stepped into Trump's line of fire this week.

Trump has been livid at Sessions for months for recusing himself from the Russia investigation, belittling him publicly and privately but not yet moving to dismiss him. But Sessions on Thursday appeared on the cover of Time magazine, Trump's favourite publication.

Trump has been known to boast about his appearances on Time covers - fake ones have been installed at his golf courses - and was angry last year when former chief strategist Steve Bannon appeared on one. One Trump ally said the President has previously said, only half-jokingly, that he should appear on the cover every week.

AP