Invictus bosses are said to be considering inviting Charles to the opening or closing ceremony as well as sporting events, where he could meet competitors.
Another royal source said the monarch, 77, would also be receptive to further opportunities for private family contact following years of strained relations.
The insider claimed: “Charles is understood to be open to anything that allows those family relationships to develop in a calmer and more positive direction. “There has been so much tension and so much said publicly over the years that nobody inside the royal circle expects everything between father and son to suddenly return to how it once was.
“One of the most important things for the King is the possibility of having a meaningful relationship with Archie and Lilibet. He has missed a considerable part of their childhoods, and there is a genuine desire for him to have more opportunities to see them and get to know them as his grandchildren rather than having that relationship conducted largely from a distance.”
“The recent family contact was important precisely because it represented a step rather than some miraculous solution to every disagreement. There is an understanding that rebuilding trust after years of difficulty takes time, particularly when the relationship has played out under such intense public scrutiny,” they continued.
“The feeling is that smaller, private encounters and carefully managed occasions could gradually make things easier. Nobody wants to place enormous expectations on a single meeting or public appearance because that would put unnecessary pressure on everyone involved.
“If Charles and Harry can continue having contact and the King can spend more time with his grandchildren, that is regarded as meaningful progress in itself. The hope would be that each positive encounter makes the next one easier and gradually creates the foundations for a more settled family relationship.”