Prince Harry has previously voiced his frustration at not being able to talk to his father, particularly when there were concerns about the King’s health.
“There’s no point continuing to fight any more, life is precious,” Harry said in his BBC interview.
The apparent meeting between the King and Prince Harry comes after rumours of efforts to resolve the family divide.
Representatives of Prince Harry and Buckingham Palace had been photographed together in a meeting in London in July, producing newspaper headlines about a “peace summit”.
But there have been no signs of Prince Harry meeting Prince William during this week, with the brothers carrying out separate arrangements.
On Monday, Prince Harry had laid a wreath at the grave of his grandmother, Queen Elizabeth II, on the third anniversary of her death.
Less than 10 miles away, Prince William and Catherine had attended a Women’s Institute meeting honouring the memory of the late Queen.