The publication reports the couple are "considering" keeping Princess Charlotte at home until schools are expected to fully reopen in the UK's summer months.
Recently both royals shared how they are coping as parents during the Covid-19 lockdown.
During a call with charity the Peek Project, William agreed with community chef Charlie Farally, who said: "You'll know yourself, the hardest time is dinner time."
The BBC reports Williams replied: "It depends what's on the table.
"If parents put something on that children love, dinner time goes very well.
"But if you put something on the table they don't want to do, that's another ball game."
Kate Middleton shared in an interview with ITV's This Morning: "George gets very upset because he wants to do all of Charlotte's projects ... making sort of spider sandwiches is far cooler than literacy work."
The Duke of Cambridge spoke about his mental health after becoming a father for a new BBC documentary, The Telegraph reports.
"I think when you've been through something traumatic in life - and that is, like you say, your dad not being around, my mother dying when I was younger - the emotions come back in leaps and bounds.
"Because it's a very different phase of life and there's no one there to kind of help you. I definitely found it very, at times, overwhelming."