The group travelled to Spain in October, but have not come back.
Alex Batty, who turns 12 today, was due to arrive back in the UK with mother Melanie Batty, 37, and grandfather David Batty, 58, on 8 October.
They had flown into Malaga Airport on 30 September to stay in the Benahavis area near Marbella, but police believe they may then have headed towards Melilla in Morocco via the port of Malaga.
Ms Batty and her father – neither of whom have parental guardianship of Alex – previously lived on a commune with the boy in the north African country in 2014.
The boy’s grandmother and guardian, 62-year-old Susan Caruana, believes this pursuit of an “alternative lifestyle” is what lies behind his disappearance.
Recalling the day they were supposed to return to the UK, Mrs Caruana said: “I got this message on Facebook and it was a YouTube video of the three of them.
“They all spoke on it and Melanie said the reasons why they had done what they had done.
“Alex said it was a million times better being with his mum and granddad. Obviously it hurt a bit but then my other concerns kicked in.
“The reason I believe they have done this is because basically my lifestyle, my belief systems, are not what they agree with – just simply living day to day, how normal people do.
“They didn’t want him to go to school, they don’t believe in mainstream school.”
Greater Manchester Police have carried out extensive enquiries, including an international public appeal, in a bid to locate Alex, who is from Oldham.
While officers do not believe he is at risk of immediate harm, they are concerned for his welfare.
Ms Batty and Mr Batty are believed to still be with him and are wanted in connection with his abduction.
Detective Sergeant Pete Morley said: “His grandmother Susan is beside herself with worry. She’s gone from seeing Alex every day to not hearing off him for months.
“She misses him terribly and is desperate to know he is alright.
“I would implore any of Melanie’s or David’s friends, who might have heard from them, to please contact police immediately. Alex’s friends may have also heard from him.
“I understand this is an emotive situation but ultimately Alex should be at home in Oldham and there are genuine concerns about his welfare.
“He has been missing out on school and we don’t know how the family are funding their lifestyle abroad.”
Alex is described as white, about 5ft tall, with blonde hair and a northern accent.
:: Anyone with information about their whereabouts should call police on 0161 856 8972, or Crimestoppers anonymously on 0800 555 111.