Meghan Markle, 36, and Prince Harry, 33, will be arriving in Cardiff on Thursday, where the Suits actress will greet locals and tour the Welsh city.
Meghan has recently visited Nottingham and Brixton where she received a warm reception from Britons.
However, a scheduling clash is said to have angered Prince William and Kate Middleton, both 35.
Mail Online reported that Harry and Meghan will visit Wales on the same day that William will carry out engagements elsewhere.
Prince William was said by the news website to be visiting Evelina Children’s Hospital to support the launch of the Step into Health programme.
A source said: “Mark my words, William will be furious.
“He is carrying out these visits because he really believes in the projects.
“Inevitably, Meghan will attract all the media attention. William understands that, so he will be very frustrated that the engagements were arranged for the same day.”
The Mail Online reported that a Kensington Palace spokesman said: “They will regularly be attending events on the same days.”
However, according to their official diary, Prince William will visit the hospital in London on January 19, which is this Friday.
However, the Duke and Duchess of Cambridge will visit Coventry on January 16.
Kate Middleton is due to visit the Mittal Children’s Medical Centre at Great Ormond Street Hospital and Bond Primary School on Thursday.
It is not unusual for royals to attend events on the same day.