Donald Trump is threatening to create a huge headache for Sir Keir Starmer by rejecting the UK’s top two choices as ambassador to the USA.

Republican sources have revealed the new US President could turn down the appointment of former Foreign Secretary David Miliband as our man in Washington.

It follows warnings that Mr Trump could reject Peter Mandelson, the Labour grandee who is Downing Street’s official choice for the role.

Mr Miliband, who once stood for the Labour leadership, is understood to have lobbied Number 10 to give him the job if Lord Mandelson is unable to take it up.

An ally of the President said: “Trump doesn’t like Peter Mandelson, but he has no time for David Miliband either.

“These lefty political appointments are bizarre.”

They suggested the outgoing ambassador Dame Karen Pierce should have been kept in the job, adding: “Miliband would never get to be ambassador. No one called Miliband will stand a chance.”

The president has to accept “letters of credence” before an ambassador can take up their post in Washington. This is usually a formality but Mr Trump has repeatedly shown he is willing to break with convention as well as to get tough with Britain, one of America’s closest allies, and could veto the UK’s deal to hand over the Chagos Islands, where there is a joint US-UK military base, to Mauritius.

However, he held out an olive branch to Sir Keir today – and said he was weighing up making his first overseas visit of his second term in the White House to the UK, although Mr Trump pointedly said he could head to the Middle East instead.

Speaking to the BBC onboard Air Force One, Mr Trump said he would have a phone call with the Prime Minister “over the next 24 hours”.

He said: “I get along with him well. I like him a lot.

“He’s liberal, which is a bit different from me, but I think he’s a very good person and I think he’s done a very good job thus far.

“He’s represented his country in terms of philosophy.

“I may not agree with his philosophy, but I have a very good relationship with him.”

The President added the UK was being considered as the destination for the first international trip of his second term.

He said: “It could be Saudi Arabia, it could be UK. Traditionally it could be UK.”

Sir Keir most recently met with Mr Trump at Trump Tower in New York during the presidential campaign.

The pair also spoke on the phone following Mr Trump’s election victory, with Downing Street saying both men agreed the relationship between the UK and the US was “incredibly strong” and would “continue to thrive”.

Following Mr Trump’s inauguration on January 20, Foreign Secretary David Lammy indicated Sir Keir would visit Washington within weeks.

Mr Trump’s close ally Elon Musk has heavily criticised Sir Keir in recent weeks as the billionaire owner of Tesla and SpaceX piled pressure on the Prime Minister to order an inquiry into grooming gangs.