The Prime Minister will be the first foreign leader to meet the US president on Friday and is likely to press the case for a post-Brexit free trade agreement between the two countries.
Moves could be made to cut tariffs on existing imports and exports and on easing restrictions on Britons who want to work in the US and vice-versa, according to the Daily Telegraph.
Mrs May has already said the pair could look at removing barriers to trade before striking a formal agreement once the UK becomes free to do so after Brexit.
The PM has also insisted Mr Trump was looking for “early” talks on a free trade deal despite concerns over his “America first” strategy.
She told BBC One’s Andrew Marr Show on Sunday: “He and people around him have also spoken of the importance of a trade arrangement with the United Kingdom and that is something they are looking to talk to us about at an early stage, and I would expect to be able to talk to him about that alongside the other issues I will be discussing with him when I am in Washington.”
The Oval Office summit will also examine global issues like tackling terrorism, the Syrian civil war, relations with Russia and the role of Nato.
Mrs May told Nato secretary general Jens Stoltenberg on Sunday that during the meeting she would emphasise the importance of the military alliance for collective defence and highlight the need for it to respond to modern threats like terrorism and cyber security.
The PM and Mr Trump could also make the case for other Nato countries to match their commitment to spend at least 2% of GDP on defence.
Downing Street said the talks would mainly be an opportunity to “get to know one another” and “establish the basis for a productive working relationship”.
Mrs May has stressed she will tell Mr Trump when she finds his behaviour “unacceptable” - a criticism she has already levelled at him over his suggestion that his fame allowed him to grab women “by the pussy”.
The president’s numerous highly controversial remarks about women inspired more than a million people to join anti-Trump women’s marches in Britain, the US and around the world on Saturday.
Mrs May said being the first world leader to hold talks with Mr Trump is the “biggest statement” she can make about the global role of women.
The Prime Minister will travel to the US on Thursday when she will become the first foreign serving head of state or government to address the annual congressional Republican retreat, when it gathers for its 30th anniversary in Philadelphia.
Her early meeting with the president will be seen as a major coup following an uneasy start to relations with Mr Trump following November’s election.