Mr. Trump has also floated a few other names as he searches for someone “big” for the role.

One is Wall Street billionaire Marc Rowan and the other is former Federal Reserve Governor Kevin Warsh, described by Mr Trump as “smart and handsome”.

The infighting was no surprise to Jeff Lord, who worked in the White House under Reagan.

“Washington is like a club,” Mr. Lord told the Telegraph.

“If you come from outside the club, everyone is going to give you grief.

“This is particularly the case of Elon Musk. He’s a genius and he has Trump’s ear. But it gets distorted.”

Thomas Whalen, associate professor of social sciences, told the Telegraph: “There are always rivalries, but in the transition team it is unusual. »

He added that Mr. Trump had organized his ministerial selections like a “celebrity apprentice reality show.”

“Given (his selection’s) marginal reputation on the political spectrum, it is not surprising that you receive pushback, even from the new Republican-controlled Senate.

“This looks like a radical takeover of the federal government and his Cabinet choices reflect that.”

The Telegraph has contacted the Trump transition team and Mr Epshteyn for comment.