The Prime Minister will also give the U.S. President a personal tour of the Churchill War Rooms after difficult talks at Number 10 Downing Street.
The two leaders are set to clash over three flashpoints - Brexit, Huawei and Iran - during two hours of deliberations in Downing Street.
The charm offensive comes after claims that Trump snubbed the outgoing May by deciding not to have a formal one-to-one meeting with her.
Time is usually set aside for visiting presidents to talk privately with the Prime Minister of the day, but the pair will sit down with their delegations with them throughout.
The Sun can reveal TV chef Jason Atherton has been drafted in to cook the president a lunch of crab and Lake District beef fillet for the leaders.
A protegee of Gordon Ramsay, the 47 year-old Atherton is famed for his intricate dishes, and recently opened a Michelin-starred restaurant in New York.
As her formal gift to America’s boss, the PM will also hand over a unique framed copy of the Atlantic Charter, agreed by Winston Churchill and President Franklin D. Roosevelt in 1941.
The document, which set out the founding principles of the United Nations, is annotated by Britain’s wartime PM, who Trump hugely admires.
May will then lead him from Downing Street to Churchill’s underground bunker complex below the Treasury, where he took many key World War Two war decisions.