May is likely to hold her talks with the new US President in the Oval Office on Thursday on what is likely to be a two-day visit to Washington.
"PM May hopes to fly out to Washington DC on Thursday - much earlier than previously thought. The visit has been brought forward after Steve Bannon, Mr Trump's chief strategist, reached out to appeal for an early trip," according to 'The Daily Telegraph' newspaper, which quoted government sources.
The plans have been secretly worked up over the last week, with officials across UK government corridors involved in the final 48 hours before the inauguration of Trump on Friday.
The new US administration has expressed an interest in reviving the close relationship enjoyed by former US President Ronald Reagan and former British PM Margaret Thatcher in the 1980s.
"They are really, really keen to capture the Reagan- Thatcher idea: A new populist in the White House and a strong woman in Number 10. They want to rekindle that as soon as possible," a government source told the newspaper.
Trump was sworn-in as the 45th US President on Friday in a gala ceremony in Washington DC.
In a statement issued by Downing Street after the inauguration, May said: "From our conversations to date, I know we are both committed to advancing the special relationship between our two countries and working together for the prosperity and security of people on both sides of the Atlantic.
"I look forward to discussing these issues and more when we meet in Washington."
UK foreign secretary Boris Johnson also offered "warmest congratulations" to Trump and said the UK wants to work "hand in glove" with the new leader.
"I want to offer my warmest congratulations to President Donald Trump on accedingto the most important political office in the world and I know that billions of people will be willing him to succeed in the months and years ahead in the very great challenges that he faces.
"We in the United Kingdom will work hand in glove for the stability, the prosperity and the security of the world with President Donald Trump," he said in a statement.
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