Princess Eugenie, Prince William's cousin, has also been telling friends the baby is a boy, according to another royal insider quoted by the Sunday People.
"They won't reveal anything to anyone - not even Harry. Of course, Harry's been making up crazy suggestions and winding them up too," the source said.
"The close inner circle all know that it's a boy and they're busily buying gifts with a boy theme. There will be an awful lot if blue in their house."
Although the royal couple have kept mum about the baby's name, Kate, 31, has accidentally dropped a couple of hints about the sex of the child in recent months.
In March she appeared to suggest a girl was on the way when she given a teddy by a well-wisher during a walkabout in Grimsby.
"I will take that for my d.." - she said, stopping herself. A nearby listener said: "You were going to say daughter, weren't you?" Kate replied: "No, we don't know."
A few days later Kate appeared to drop another clue as she revealed she had bought a Bugaboo pram in light blue which could indicate the newborn would be a boy.
The pram's colour came to light when Kate chatted to a group of Army wives at a reception on St Patrick's Day.
Then Prince Harry was seen holding a blue teddy bear as he walked to Kensington Palace, the home he shares with Kate and William in London.
But there was a simple explanation - the bear had been given to him by a little girl while he toured Nottingham. She asked him to give it to Kate's baby and he delivered it in person.
But another insider added: "Even though there's a lot of gossip doing the rounds, there's no way anyone can confirm it at the moment."
No decision has been made where Kate will have the baby, but the choice has been narrowed down to two hospitals, according to reports.
Princess Diana Prince had William and Harry at St Mary's hospital in Paddington, West London, while there is speculation that the child could be born at the Royal Berkshire Hospital - the birthplace of Kate and her sister Pippa.
- DAILY MAIL