For William, “family comes first,” as a close friend tells PEOPLE. Like Kate, he has been prioritizing trying to keep things as normal as possible for their children amid his wife’s illness.

The new report in The Sunday Times comes as William returned to royal duty after a summer break on Sept. 5 in London.

On Tuesday, Sept. 10, William will visit Llanelli in west Wales, where he will spend time with schoolchildren, the local air ambulance crews and the national women’s rugby team.

On Sept. 12, he will represent his father, King Charles, when he attends the Sovereign’s Parade at the Royal Air Force College in Cranwell, Lincolnshire. The parade will include four International Officer Cadets from Jordan, Kenya, Pakistan and Uganda.

Next week, William is set to visit Aberdeen to check on the progress of his Homewards campaign to help the unhoused. He is also planning to be in Cape Town for the Earthshot Prize in November.