Prince Philip summoned Charles to the hospital just weeks before he died to "brief him" on what he had to do as the family's next patriarch, it is claimed.
The Prince of Wales, 72, looked close to tears as he walked behind his father's coffin with other senior royals before the Duke of Edinburgh's funeral on Saturday.
The heir-to-the-throne will reportedly hold a royal summit to decide the future of the monarchy over the next two generations after Philip, 99, died peacefully in his sleep at Windsor Castle on April 9.
In one of his first acts in his new role as the Royal Family's patriarch, Charles' decision to have senior royals walk back to the castle's private apartments allowed feuding sons William and Harry a possible moment of reconciliation, an expert claims.
There were claims that Charles, William and Harry spent two hours speaking in private after the funeral.
Another expert suspects the Queen likely wasn't in the mood to host a family summit to address the fallout and anger over Prince Harry and wife Meghan Markle's explosive interview with Oprah Winfrey.
Philip died just weeks after he was released from a London hospital - the final time he was seen in public - following heart surgery and treatment for an infection.
It is said that the frail duke summoned Charles to the hospital and had three important things to say during a bedside heart-to-heart.
Fully aware he was unlikely to recover, Philip told the eldest of his four children to take care of the Queen, explained how to lead the family following his death, and expressed his desire to die in his own bed at Windsor Castle, where he and the monarch had been shielding during the Covid pandemic, the Mail on Sunday reported.
"This heart-to-heart marked not just the ending of a long and successful era, a changing of the guard, but a much-changed relationship between father and son, too," the royal biographer Robert Jobson wrote.
The Sun's photographer, Arthur Edwards, said during an appearance on ITV's Lorraine that the duke "made all the big decisions" and advised his son on what would happen next.
Mr Edwards told host Lorraine Kelly: "Can you imagine that conversation in the hospital three weeks before, when he was summoned by Prince Philip to come?
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"It must have been a lot of plain speaking there, what he was expected to do, arrangements for the funeral.
"I think the duke knew he was on the last leg and he was briefing his son, 'this is what you've got to do, son'."
Charles and William, 38, will hold a summit to decide the future of the monarchy over the next two generations, the Telegraph reported.
In consultation with the Queen, the next two kings will decide how many full-time working members the family should have, who they should be, and what they should do, sources told the newspaper.
Former royal correspondent Richard Kay wrote in the Daily Mail that Charles' "off-the-cuff decision" to have the royals walk back to the castle's private apartments after Philip's funeral at St George's Chapel on Saturday "turned out to be a masterstroke".
He added: "This could have been a moment of risk, instead it allowed us the first glimpse of the possibility that somehow William and Harry can put their bitter split behind them and rebuild that once whisper-close bond.
"It is hard to read too much into this encounter, for it was all too brief, but if there is to be reconciliation between the brothers, this was surely the moment of its inception."
Queen 'not in mood'
Author Ingrid Seward claims any kind of family summit involving the Queen, at this stage at least, to address the Oprah interview and other issues at the heart of the rift would be unlikely.
She told the Times: “His (Harry's) grandmother will not be in the mood for it. She hates confrontation.
"The children have much difficulty getting the Queen to discuss anything other than dogs or horses.
“I remember Fergie telling me it took three weeks for them to try and get her to discuss their divorce. She kept saying ‘Oh, I’ve got to take the dogs for a walk’.”
Harry, 36, returned to the UK without his wife Meghan, 39, and their son Archie, who turns two next month, for his grandfather's funeral.
He and William did not walk shoulder to shoulder behind Philip's coffin before the funeral on Saturday.
Their cousin, Princess Anne's son Peter Phillips, 43, walked between them in a formation approved by the Queen.
Harry, William and Kate Middleton, 39, were seen chatting after the service, and the Duchess of Cambridge played "peacemaker" as she slipped away to allow the brothers some time to talk alone as they walked away from the chapel together.
Sources told the Sun that Harry spent two hours speaking with William and Charles in private following the service.
But Mr Kay said talk of a family summit or Charles pulling his sons aside was "wide of the mark".
Queen's 'loneliest' birthday
The Queen, meanwhile, faces her loneliest birthday - her first without Philip in seven decades - when she turns 95 on Wednesday, just four days after the funeral and 12 days after the Duke of Edinburgh died.
Coronavirus lockdown rules forced her to sit alone at the duke's funeral, an image that left the nation heartbroken.
Still in an official two-week period of mourning, the Queen is expected to have video calls with family, including William and Kate's children, who have gone back to school in London following the Easter break.
Public events to mark the birthday have been shelved or toned down.
The royals have agreed a rota to visit her ahead of her birthday, sources told the Mirror.
She is staying at Windsor with around 20 staff members, dubbed HMS Bubble.
Royal sources confirmed the Queen is expected to have a series of regular visitors as she continues to live at Windsor Castle, where she spent the majority of the last 13 months living with her darling Philip.
One source said: “The Queen will not be alone.
“She will have others who care about her deeply and want to be there to support her in her most pressing hour.
“In typical fashion the Queen has insisted she is coping and despite the suggestion she had prepared herself for this day to come, everyone is well aware there is nothing like the experience when it comes.”
Charles is expected to visit his mother this week, taking the 90 minute drive from his country home Highgrove in Gloucester.
Princess Anne will also pop in from her home in Gloucestershire, Gatcombe Park while the Countess of Wessex, who has for years enjoyed a fabulous relationship with the Queen, has planned several visits in the coming days with her children Louise, 17 and James, 13.