King Charles was said to be ready to forgive his son for public criticism of the Royal Family.
But Prince Harry stayed at a hotel instead, The Sun claims.
He had flown 5,000 miles from the home he shares with wife Meghan and their young children Archie and Lilibet in Montecito, California earlier this month.
Harry, 39, appeared at a WellChild charity event in Chelsea, west London before jetting to Dusseldorf, Germany the next day for the Invictus Games - meaning he spent September 8 on his own.
The newspaper claimed the King’s office formally offered royal accommodation and security for his one-night stopover.
A spokesman for Harry and Meghan was contacted for comment by the Evening Standard, but it is understood the prince’s already busy itinerary made it impossible to accept.
Charles and Queen Camilla marked the first anniversary of Queen Elizabeth II’s death with a poignant moment of prayers and reflection in the Balmoral church where she worshipped.
Harry was hundreds of miles away in Windsor, where he visited St George’s Chapel at the castle, to pay his respects.
An image of Harry leaving St George’s that morning was circulated on social media.
Ingrid Seward, editor-in-chief of Majesty Magazine, told The Sun “For Harry this was a golden opportunity missed.
“He should have braved it out and gone to see them. If the King invites you to Balmoral, then most people would cancel all of their travel plans.
“He could have easily rearranged things slightly to allow himself the time.
“Any attempts for a rapprochement must be on the King’s terms. I’m glad he is showing some backbone and offering this olive branch.”
The Duchess of Sussex, 42, made an impromptu speech when she arrived at the Invictus Games on September 12.
Meghan and Harry appeared on a stage and appeared in high spirits as they spoke during a party for friends and family of competitors.
Harry launched the sporting event for wounded military personnel and veterans.
The couple appeared in public together for the first time at the Toronto Invictus Games in 2017, pictured hand in hand at a wheelchair tennis event.