The couple divide their time between London and Los Angeles and though six-year-old Teddy has been studying at a private school with campuses in both cities, her parents - who also have Charlie, four, and eight-month-old Coco together - are worried it will be too disruptive for her as she gets older so plan to take her out of mainstream education.
A source told The Sun newspaper: ''They have decided home-schooling is the way forward.''
The 'Angels' hitmaker previously insisted he wouldn't want his children to go to an American school because they were full of ''f***ing idiots''.
Speaking before he became a dad, the former Take That singer said: ''I think kids there have a massive sense of entitlement, are dull, and dumb.''
The 45-year-old pop star recently admitted his life has changed a lot and become ''much better'' now he's a parent.
He said: ''Back in the 90s, it used to be strippers and cocaine and now it's hummus and celery and my life is much better for that. I used to live on rock star hours, which was go to bed at three or four o'clock in the morning, and wake up in the afternoon. You quickly realise when you have a child you are not an insomniac but a bit lazy and prone to exaggeration.''
Meanwhile, Robbie previously revealed he has swapped cigarettes for crayons and has found colouring in pre-drawn pictures is helping to relieve his cravings because it gives him something to focus on other than how much he's missing smoking.
Speaking in an Instagram Live video, he said: ''I'm just doing some colouring in, which is good because I've got something to concentrate on. Art is good for my mind. Anyone who is giving up smoking with me, keep on. The struggle is real. I've been all right all week, it's been sort of six out of ten difficult and then in the last hour and a half I've just collapsed, panic attacks, over- whelmed ... I've had to get out of the house just to calm down a little.''
Ahead of their upcoming tour, and prior to the release of their long awaited album, Smoke Fairies played a great warm-up gig at Elsewhere in Margate.