Speaking on CNN, Mr O’Brien commented: “Trump likes advocates. He likes loyalists. He likes people who will advocate his viewpoint. He doesn’t like people who get more airtime and more attention than he does.”
Mr Bannon, former chairman of the far-right news outlet Breitbart, is known for voicing his opinions on Muslims, immigration and refugees.
Yet since the election, Mr Bannon has kept a low profile, and has rarely spoken in public.
“Bannon is a survivor,” said Mr O’Brien. “He’s clearly stayed in the background; he doesn’t like to give interviews for the most part.”
This has changed over the past week. Mr Bannon was thrust into the spotlight when he was promoted to an influential position on Mr Trump’s National Security Council.
It has also been claimed that he was a key driving force in drafting Mr Trump’s widely criticised immigration order.
The fierce backlash against the executive order, combined with his apparent influence in the White House, has prompted a flurry of publicity as outlets speculate over the extent of his power.
This has included Mr Bannon’s appearance on the cover of Time magazine, along with the headline: “Is Steve Bannon the Second Most Powerful Man in the World?”
According to Mr O’Brien, this won’t sit well with the President, warning that stealing the limelight from Mr Trump has proved to be the "kiss of death" for previous advisers.
Rudy Giuliani and Chris Christie both played key roles in Mr Trump’s inner-circle during the 2016 presidential campaign, only to quietly disappear from view after receiving extensive media coverage.
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