Downing Street moved to try and play down the significance of the Ukip leader's meeting with Trump.
A spokesman for May said that No 10 "has been consistent that Farage has no role" in the Government's relationship with the in-coming US administration.
Farage was seen getting into a gold-plated elevator at Trump Tower with Raheem Kassam, who made a bid to be his replacement at Ukip, only to take himself out of the running last month.
The meeting came after Farage said he would do "very well" as the US ambassador to the EU if given the chance.
Farage publicly supported Trump's Presidential campaign and joined him on the trail at a rally in Jackson, Mississippi, where he was introduced by his friend as "Mr Brexit".
Such is his fondness for the Republican that he even watched the election results come in at the US presidential night party at the US embassy in London, before catching an early morning flight to America.
Earlier this week, on LBC Radio, Farage said: "Is he going to offer me a job? I'm hoping he might do.
"He will be in need of a proper Eurosceptic ambassador in Brussels for the European Union. I would rather like that job."
He added: "Being a foreigner will not disqualify me. As long as we can bring the EU down, it doesn't matter how we do it."
Farage, who is serving as interim Ukip leader until next month, said he would do the job 'very well' having been an MEP in Brussels for nearly two decades.
During a US visit, he was asked on Fox News why Trump should meet the PM after the things senior Tories had said about him.
He said: "I think he has got to meet her. Mrs May's team have been quite rude about Trump, so there are some fences to be mended.
"Trump is an Anglophile, he understands and recognises what our two great nations have done together between us.
"And, thank goodness, we are coming towards the end of an American president who loathed Britain.
"One of the things we can do, we can have between us a sensible trade relationship, cut tariffs, we are massive investors in each other's countries. There's a bright future."
The interim Ukip leader has suggested that 'insulting' comments about Trump by senior Tories may have been the reason why May was only tenth on the President-elect's list of foreign leaders to call after his surprise win last Tuesday.
His remarks came after it emerged May's two joint chief's of staff had attacked Trump on social media before taking up their current posts.
Fiona Hill posted last December: "Donald Trump is a chump," while her colleague Nick Timothy wrote in March: "American politics was depressing enough before Trump took off."
I commend @realDonaldTrump for the courage with which he has fought this campaign & look forward to a closer relationship between USA & UK.
Foreign Secretary Boris Johnson was scathing about Trump's attitude to Muslims while he was mayor of London last December, saying: "I think Donald Trump is clearly out of his mind if he thinks that's a sensible way to proceed, to ban people going to the United States in that way, or to any country.
"What he's doing is playing the game of the terrorists and those who seek to divide us. That's exactly the kind of reaction they hope to produce.
"I think he's betraying a quite stupefying ignorance that makes him frankly unfit to hold the office of President of the United States."
While pushing for a meeting between the President-elect and May, the interim Ukip leader appeared to make light of a now infamous 2005 videotape of Trump in which he boasted about being able to grope women because of his celebrity.
"I will be encouraging him to make the UK his priority. I am now going to become a diplomat - 'Come and schmooze Theresa, don't touch her for goodness' sake'. If it comes to it I could be the responsible adult and make sure everything's okay," he told TalkRadio.