Harry has not seen his father in over a year and is reportedly open to meeting Charles, who has been receiving cancer treatment since early 2024.
The King is thought to be in London having travelled from his Balmoral home where he has been spending his northern hemisphere summer break.
His son is visiting the Centre for Blast Injury Studies at Imperial College London, an institution he has close connections with having opened its laboratories in 2013.
Harry has been carrying out a string of events since arriving back home on Monday and beginning a four-day working stay by leaving flowers at the final resting place of his grandmother Queen Elizabeth II to mark the third anniversary of her death.
His visit has reignited commentary about the state of his relationship with senior members of the royal family.
He remains estranged from his older brother Prince William, who is travelling to Cardiff to learn about a pioneering mental health hub on World Suicide Prevention Day, with no prospect of the pair meeting.
In February last year Harry made a transatlantic dash from his Californian home to the UK to see his father following his cancer diagnosis.
The move showed both sides were willing to put their strained relationship on hold and since then there have been further developments.
Senior aides to Charles and Harry were pictured in the Mail On Sunday during a meeting in London this summer that was reportedly a step towards restoring the relationship between the duke and the royal family.
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