It will be his first visit to Britain since early February, when he dashed across the Atlantic to see the King shortly after his cancer diagnosis was made public. On that occasion, father and son spent little more than half an hour together behind closed doors at Clarence House.
The Duke will no doubt hope to see his father again next week, should their diaries permit. It is thought Charles will make time to see his son if he is able.
But on Wednesday, the King will have his weekly audience with the Prime Minister before he hopes to attend the first Buckingham Palace garden party of the season, medical advice pending.
Charles is also understood to have various appointments and engagements scheduled for the rest of the week.
The Duke revealed in an interview with ABC News in February that he was “grateful” for the time spent with his father that month, adding: “I’ll stop in and see my family as much as I can.”
But he is unlikely to leave the US before Tuesday because the previous day is Prince Archie’s 5th birthday, which he will want to celebrate with his family.
Harry missed most of his son’s 4th birthday last year because it fell on the same day as the King’s coronation. The reason given for his swift return to the US after the Westminster Abbey ceremony was his desire to kiss his son goodnight on his special day.
It is thought the Duke might extend next week’s visit a little longer than more recent flying visits, not least because it is a working trip and one that has been in the diary for some time.
He may take the opportunity to schedule meetings with representatives from the various UK-based charities he supports, such as WellChild, the Diana Award and Scotty’s Little Soldiers.
He might also want to catch up with his friend Johnny Mercer, the veterans minister, who is spearheading the UK’s bid to host the 2027 Invictus Games in Birmingham.
There is no suggestion he will see his brother the Prince of Wales, who is in Windsor with his family while the Princess of Wales undergoes chemotherapy.
Prince William also has a busy diary next week, with a series of public engagements. It is thought he may conduct an investiture next Wednesday that would allow him to confer an honour on the mother of a close friend, Henry van Straubenzee, who died in a car crash in 2002, aged 18.
In January, Claire van Straubenzee was awarded an MBE for her charity work and her husband, Alex, and their two other sons, Thomas and Charlie, both of whom remain close to William and Harry, are expected to join her at Windsor Castle for her investiture.
After the Princess of Wales released a video message on March 22 revealing she was undergoing treatment for cancer, the Sussexes were said to have made contact with the couple “privately”. They also issued a public statement saying: “We wish health and healing for Kate and the family.”
The Duke’s forthcoming visit will be his first since losing a £1 million ($2m) High Court battle in February over the decision to deny him the right to automatic police protection.
In his witness statement, Harry argued his children could not “feel at home” in the UK if it were “not possible to keep them safe”.
The Duke is due to give a reading at the Invictus Games service. Actor Damian Lewis will recite the Invictus poem, written by William Ernest Henley, of whom there is a memorial bust within the crypt of St Paul’s Cathedral.