The lunch will take place on June 3 the first day of Trump's three-day state visit to the UK.
Prince Harry's wife Meghan, the Duchess of Sussex, is not expected to attend the lunch as she has not resumed public engagements since the birth of their son Archie Harrison, CNN reported.
The Buckingham Palace last week revealed the schedule for Trump's three-day visit.
The US President and the First Lady will be officially welcomed at Buckingham Palace in London by the Queen, Prince Charles and his wife Camilla, the Duchess of Cornwall.
The Queen will then host a private lunch for her guests before inviting them to view a specially curated exhibition, showcasing items of historical importance to the US.
Trump and Melania alongside Andrew, the Duke Of York, will also visit Westminster Abbey to lay a wreath at the Grave of the Unknown Warrior.
The US leader will have a breakfast meeting with outgoing UK Prime Minister Theresa May along with senior UK and US business leaders.
On June 5, the Queen along with Prince Charles and her visitors will attend commemorations for the 75th anniversary of the D-Day landings at Southsea Common in Portsmouth.
The event where over 300 World War II veterans will also be present will include a musical performance, readings and military displays, including a flyover of 25 modern and historical aircraft.
From the UK, the Trumps will travel to Normandy on the invitation of French President Emmanuel Macron to continue D-Day commemorations.
Trump and Macron will also hold a bilateral meeting.
Trump will also visit Ireland for a meeting with Irish Prime Minister Leo Varadkar.
( With inputs from IANS )