"Many people would like to see @Nigel_Farage represent Great Britain as their Ambassador to the United States. He would do a great job!" Trump said in a tweet today.
Trump and Farage, the leader of the UK Independence Party (UKIP), have very good relationship.
Farage was often seen by Trump's side during the election campaign and was among the first to fly out to the US to meet the President-elect after the election.
While Farage said he was "very flattered", Downing Street in London issued a statement dismissing any such possibility.
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"There is no vacancy. We have an excellent ambassador to the US," the statement said in reference to Sir Kim Darroch.
Darroch, formerly the UK's national security adviser and permanent representative to the European Union, took over the role in January.
Farage said he had not been expecting Trump's tweet, but described it as a signal that Downing Street needed to change its thinking about him.
"They all say the same thing: that Trump is a very loyal man and supports those that stand by him," he said.
Repeating his offer of help, which had been rejected by Downing Street on multiple occasions, Farage said: "The world has changed and it's time that Downing Street did too."
The British leader is likely to attend the January 20 inauguration of Trump as the 45th President of the US.
It is unprecedented for an incoming US President to ask a world leader to appoint an opposing party leader as ambassador, and Trump's tweet would put British Prime Minister Theresa May in a slightly difficult position.
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