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.
The palace source played down suggestions that Prince William was "furious" with his brother after the documentary aired on Sunday.
It followed Prince Harry's admission in the film that he and William have "good days" and "bad days".
Asked about media reports of a rift between the brothers, the Duke of Sussex said that "inevitably, stuff happens" as a result of "this family being under the pressure that it's under".
He added: "We are brothers. We will always be brothers.
"We are certainly on different paths at the moment, but I will always be there for him as I know he will always be there for me."
Alarm bells are ringing. This morning a well-placed source told the BBC that Prince William was 'furious' with his brother about the interview he gave.
A palace source said that was not his understanding of the prince's mood. Instead the official suggested a mood of concern, for the safety of the couple.
The interviews revealed two people under considerable pressure, such pressure that they were prepared to go public with their concerns; Harry still struggles with his mental health; the shadow of his mother, Diana, Princess of Wales still looms over his life.
Worst of all he sees history repeating itself - first the media tore down his mother, he thinks, now his wife.