The American president is said to have told organisers he wants his adult children, Donald Jr, Ivanka, Eric and Tiffany, to meet the Royal Family during the three-day state visit marking the 75th anniversary of D-Day.
Prince William and wife Kate, Duchess of Cambridge, are expected to meet the young Trumps and their partners, while Prince Charles and Camilla will reportedly be hosting a tea for Mr Trump and his wife, Melania, at Clarence House.
The Trumps will be honoured with a lavish Buckingham Palace banquet put on by the Queen on June 3.
“POTUS state visit to the UK is set to include not just the president’s children who work in the White House, but also his other adult children, per multiple people familiar with planning,” tweeted New York Times White House correspondent Maggie Haberman.
Details of the trip are reportedly still being finalised by the White House and Buckingham Palace.
Mr Trump and his wife had tea with the Queen at Windsor Castle during his working visit to the UK last summer, which sparked mass protests in central London.
This time, the couple will be joined by ‘First Daughter’ Ivanka Trump, 37, and her husband Jared Kushner, 38; Donald Trump Jr, 41; Eric Trump, 35, and his wife Lara, 36; and Tiffany Trump, 25.
Mr and Mrs Trump’s youngest son Barron, 13, is not expected to join his parents for the visit.
The Duke of Cornwall’s meeting with the president will be the first between the two men - who have conflicting views about climate change and the environment - since Mr Trump was elected in 2016.
The Trumps are not expected to stay at Buckingham Palace - unlike Mr Obama and his wife Michelle when they visited the UK in 2011 - because of £369 million renovations taking place.
Neither Buckingham Palace nor the White House have commented on the reports.
Uncertainty over the future of Prime Minister Theresa May has cast doubt over whether she will meet Mr Trump during the visit. The pair were reportedly expected to hold a joint press conference under plans briefed to cabinet this week.
In a statement, the White House said: “President Donald J. Trump and First Lady Melania Trump accepted the invitation from Her Royal Majesty Queen Elizabeth II to visit the United Kingdom from June 3 to 5, 2019.
“This state visit will reaffirm the steadfast and special relationship between the United States and the United Kingdom.”