The Duke and Duchess of Cambridge made the revelation to the Serbian tennis player after he won his fourth Wimbledon title with a 6-2 6-2 7-6 (7-3) victory over Kevin Anderson on Centre Court on Sunday.
Footage captured inside the All England Tennis Club shows Djokovic asking the Royal couple: “How are your children?”, with both Kate and William replying “very well”.
The Duke continues the conversation by saying: “Trying to get a tennis racket in their hand – and a football.”
Last October, Kate revealed four-year-old George’s love of tennis, describing how he “wants to whack a ball”.
She made this revelation when speaking to Lawn Tennis Association 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 also revealed that the Duchess asked for advice from tennis coach and Andy Murray’s mother Judy, who suggested she should just focus on tennis skills.
But Ms Murray admitted she tried to put Kate off encouraging her children to take up tennis, as “it’s a very difficult journey”.
She later said: “Williamwas saying about Prince George, Catherine trying to teach Prince George how to play tennis and how I think she had said last week that she wants him to be the next Andy Murray.
“I’m sure she was joking. I was trying to put them off that – I said it’s a very difficult journey.’
Commenting on his conversation with the Royal couple, Djokovic described having his three-year-old son Stefan see him lift the Wimbledon trophy on Sunday as a “really special moment”.
He said: “He actually came just as I was about to answer the question about my son, so it was a really special moment.
“I was nervous, I was hoping he could be there, so it’s very nice.’
For the men’s singles final on Sunday, Kate donned a £1,150 buttercup yellow dress by world renowned designer Dolce & Gabbana,
It featured a pencil silhouette that fell just below the knee and gently frilled sleeves, completing her outfit with her ‘Sicily’ handbag, nude court shoes and gold jewellery.
On Saturday, she had worn an outfit by Jenny Packham when watching the women’s singles final with Meghan Markle.