She was speaking to Lawn Tennis Association (LTA) coach Sam Richardson during a visit to the headquarters of British tennis at the national tennis centre in London.
Mr Richardson said: “She asked what kind of stuff George should be doing. He is interested in tennis but being four, he just wants to whack the ball.”
He said: “You have to wait for them to show interest.”
Richardson, who heads up the LTA’s Tennis for Kids grassroots programme, which teaches the game to children, said: “She said she had also spoken to Judy Murray, who advised her to take the racket away and just focus on skills.”
Kate, who is the LTA patron, proved to be a smash hit with tennis stars past, present and future during the visit.
Kate, who is pregnant with her third child, came dressed for action and sporting a big smile.
She sported black tracksuit bottoms with a wide white side panel, a black jersey and white trainers and took part in a gentle children’s training session.
It included an easy knockabout with some infants who were “very excited to meet a princess”, according to British number one Johanna Konta who attended as an ambassador for the Tennis for Kids grassroots scheme for five- to eight-year-olds.
Kate, who is now in her second trimester, has been stepping back into the limelight after suffering from hyperemesis gravidarum – a severe form of morning sickness.
The royal baby is due in April.
Kate joined in exercises with children including Joe Edwards, eight, from East Sheen Primary School, and said: “I used to play a lot of tennis but I’m a bit unfit now.”
She seemed in good spirits as she chatted with Konta and watched some on-court sessions.
She helped test the delighted children’s agility and reaction in a hand-tagging exercise which looked like they were giving each other high-fives from different directions.
She also retrieved low balls from the ground with her racket before hitting a button which served balls to wheelchair tennis player Alfie Hewett at 87mph.