MailOnline has contacted Kensington Palace for comment.
Five-year-old George and his little sister Charlotte, three, often join their parents at major royal events including Trooping the Colour and the Duke and Duchess of Sussex's wedding.
But Kate and William have insisted on keeping day-to-day family activities, like the school and nursery run, a private affair.
In 2016, the Duke told the BBC: "There'll be a time and a place to bring George up and understand how he fits in, in the world.
"But right now it's just a case of keeping a secure, stable environment around him and showing as much love as I can as father."
Similarly, Prince Louis, who was born in April, has only been seen in public once since his birth — at his christening at St James's Palace earlier this month.
The Cambridges recently relocated from Amner Hall in Norfolk to live at Apartment 1A Kensington Palace full-time ahead of George's enrolment at Thomas's Battersea.
Commenting on the move, a source told the Daily Mail: "They thought long and hard about where George should be educated and really liked Thomas's, which has a lovely nurturing atmosphere.
"The school focuses as much on helping develop the character of pupils, as what they learn. William and Kate are keen to allow George to spread his wings and make friends at this stage."
The source added: "They know there will come a time when they will have to sit down and talk to him about the implications of his royal status and why so many people are interested in him.
"He is becoming more aware of the cameras. But they are determined to do that at George's own pace and feel that can all wait a bit."
George celebrated his fifth birthday last weekend with his parents, grandparents, brother and sister on the Caribbean island of Mustique.