The prospect follows their private reunion at Highgrove last month, when Harry visited Britain with his wife Meghan Markle, 45, and their children Prince Archie, seven, and Princess Lilibet, five.
Sources have now claimed to Radar that even though William, 44, understands why Charles wants to rebuild his relationship with his younger son, he remains deeply wary about any reconciliation becoming a public spectacle.
Palace concerns are said to center on whether an appearance involving Harry and the King could generate another wave of publicity around the Sussexes and their relationship with the monarchy.
William has remained estranged from Harry following years of bitter accusations involving the Royal Family, including claims made during television interviews, the Sussexes’ Netflix documentary series and Harry’s memoir, Spare.
Harry has repeatedly spoken publicly about wanting reconciliation with his family.
However, he and William have shown little sign of repairing their fractured relationship, with the Prince of Wales reportedly maintaining his distance from his brother.