Prince William is said to be hoping the Duke and Duchess of Sussex "are all right" after they told an ITV documentary they were struggling.
The palace source said there was a view the couple were "in a fragile place".
Kensington Palace had no comment on the ITV film, which aired on Sunday.
The documentary followed the Duke and Duchess of Sussex on their tour of southern Africa earlier this month.
In interviews, the couple both said they were struggling with the intense scrutiny from elements of the British tabloid press.