Prince William and King Charles have held secret talks at Sandringham.
The Prince of Wales had a one-on-one meeting with his father this week.
Prince William is set to return to public duties this Sunday at the BAFTA ceremony.
The Prince of Wales will attend the Bafta award ceremony on Sunday evening in his first public appearance in 11 days.
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The possibility of William taking on some of the King's duties following the monarch's cancer diagnosis has been discussed but is not thought to be on the agenda, according to the Mirror.
The Prince of Wales is the President of the British Academy of Film and Television Arts.
William will watch the award ceremony before meeting category winners and the Rising Star Award nominees.
King Charles and Prince William's talks come as Prince Harry is prepared to take up a temporay role in the Royal Family, according to the Times.
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The Duke of Sussex flew to the UK last week and held a 45-minute meeting with the King after being informed of his father's cancer diagnosis.
The King and his youngest son are said to have shared multiple "warm exchanges" since the monarch's cancer diagnosis.
The Duke of Sussex has now told his friends that he is prepared to take on a temporary role in the Royal Family to help his father while he is unwell.
On Thursday, Harry confirmed that he will return to the UK soon as he intends to see his family "as much as he can".
The King and his youngest son are said to have shared multiple "warm exchanges" since the monarch's cancer diagnosis.
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The royal stated he has many trips planned to go back to the UK and see his family.
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The royal stated he has many trips planned to go back and see his family.
Harry told Good Morning America: "I have got many trips planned that will take me through the UK or back to the UK so I will my family as much as I can."
The Duke of Sussex was asked: "What is your outlook on his [the King's] health?"
He replied: "That stays between me and him."