It comes as the brothers continue to navigate their fractured relationship after Prince Harry and Meghan's departure from the royal family.
A royal insider told the publication, "Things are still fraught — William is still wary of spending any time alone with Harry as you never quite know what may be reported back afterwards."
Despite the snub, the Cambridges sent their niece well wishes for her birthday, which she celebrated at Frogmore Cottage on June 4. The tweet read, "Wishing a very happy birthday to Lilibet, turning one today!".
Wishing a very happy birthday to Lilibet, turning one today! 🎈
— The Duke and Duchess of Cambridge (@KensingtonRoyal) June 4, 2022
Although the royal brothers did not spend any solo time together, Prince Harry and Meghan's friend Omid Scobie reported the couple spent private time with Prince Charles and Camilla as well as the Queen before returning to the US.
Meanwhile, Harry's biographer, Angela Levin criticised the couple's decision to swiftly return to California. Speaking to the Daily Mail she said, "They should have stayed for a few days afterwards, spent time with the Queen after her duties had finished, tried to make things right with William. They would have had the time - but they chose to rush in and rush out."
Levin claimed the estranged prince has "lost all respect for anybody now", adding, "All his impatience and self-destruction is visible. He can't hide it."
During their short visit, the family stayed at Frogmore Cottage, where Harry and Meghan lived before relocating to the US. The Sussexes recently extended their 12-month lease on the property.
Renewing the lease on the abode, which was due to expire on March 31, ensures Harry can still serve as one of the Queen's four Counsellors of State, because the Windsor address qualifies him as being domiciled in the UK.
A spokesman for Harry confirmed to the Daily Telegraph: "There are no planned changes to the current arrangement".
Harry and the other Counsellors of State - his father Prince Charles, brother Prince William, and uncle Prince Andrew - are able to undertake some of the Queen's duties, including signing documents and attending Privy Council meetings at her request should she fall ill or be otherwise unavailable.