The US President floated the possibility of finding time to meet up with friend Nigel Farage and Tory leadership frontrunner Boris Johnson during the three-day state visit.
But in an apparent snub to the outgoing Prime Minister, no time was allocated for private discussions.
Foreign Secretary Jeremy Hunt, a leading contender in the race replace the premier who won praise from Mr Trump in the days before his visit, will be among those present during talks with the president in the cabinet room at No 10 on Tuesday.
After a lunch in the state dining room, Mrs May and Mr Trump will give a joint press conference where the President is likely to face questions about Brexit and the Tory leadership race.
And No 10 will be braced for the President to publicly wade into the row about the UK potentially involving Chinese firm Huawei in a major upgrade to mobile networks in the face of security warnings.
Mrs May will give the President a private tour of the Churchill War Rooms, the underground bunker where Winston Churchill led the country during the Second World War, which No 10 suggested would allow time for informal discussions between the leaders.
Conservative MP Nigel Evans said the arrangements for the meetings between the two leaders were “sensible”.
He added: “Although I do hope the Prime Minister and the President have an opportunity to have a few words in private right at the end.
“I think for nostalgia’s sake that is important.
“Clearly, the position on things like Brexit is going to be the responsibility of the new leader of the party.
“Whoever that person is ought to establish talks urgently with the President of the United States both on the trade front and also to ensure that the relationship that clearly was building between the prime minister and the president continues.”
Downing Street insisted there was nothing unusual in the arrangements for Tuesday’s talks.
The Prime Minister’s official spokesman said it was “always going to be the case” that the meeting in the Cabinet Room at Number 10 would involve the delegations from the two sides rather than just the leaders and there would be “substantial bilateral discussions”.
“These are always how the discussions take place with any leader,” the spokesman said, adding there was “nothing unusual here”.
Previous visits between prime ministers and presidents have included private one-to-one talks before – including Tony Blair and George W Bush, whose meeting at the Crawford Ranch in the run-up to the Iraq War became the subject of intense focus after the conflict.
As he boarded Air Force One to fly to the UK, Mr Trump again suggested he may find time to meet up with Mr Johnson and the leader of the Brexit Party and said they both want to see him.
President Trump will arrive for talks in Downing Street with wife Melania Trump where they will be met at the door to No 10 by Mrs May and husband Philip.
Mr May and the First Lady will then host a Downing Street garden party as a thank you for staff and embassy officials.
The Prime Minister, who quits as Conservative leader on Friday, is expected to discuss hopes for a free trade agreement between the UK and US after Brexit during the day. Trade between the two countries totalled £190 billion last year.
But diplomats have signalled accepting chlorinated chicken and access to NHS contracts could be the price to pay for securing a swift trade deal that gives better access to the huge market.
Bolstering existing business ties will top the agenda at a breakfast meeting that marks the start of the second day of the state visit.
Mrs May and Mr Trump will hold talks with leading British and American businesses at St James’ Palace, where they will be joined by the Duke of York, Cabinet ministers and their US counterparts, and Mr Trump’s daughter Ivanka.
The Prime Minister will call on the firms, which include BAE Systems, the National Grid and Goldman Sachs International, to seize the chance to boost jobs and growth.
It is a great partnership, but one I believe we can make greater still,” she will say.
“With a bilateral free trade agreement, with broader economic co-operation, and by continuing to work together to underpin, shape and influence the global economy and its rules and institutions – keeping markets free, fair and open, and keeping our industries competitive.
“There are opportunities to seize, and there are challenges we need to work together to tackle. Today, let us look at how we do both.
“Through dialogue like this we can ensure that our economic partnership not only endures but continues to grow stronger for many years to come – making our businesses more competitive, and creating jobs, opportunity and prosperity for all our people.”
Sir Roger Carr, Chairman of BAE Systems said: “Our relationship with the United States of America is long-standing and operates to our mutual benefit on the firm foundation of trust, transparency and true partnership.”