Maria was found during a raid on a Roma camp in central Greece last week.
DNA tests showed that Maria is not related to the couple, who insist they were given her legitimately.
The little girl is being cared for in Athens by a charity, called The Smile of the Child, which has received more than 8,000 calls after an appeal for information about her identity.
The Roma couple – a woman aged 40 and a 39-year-old man – are due to appear before judges later on Monday to answer charges of abducting a minor and holding false papers.
The Roma community where the girl was found has rallied around the couple, saying they looked after her well.
The head of the Roma association in Farsala in central Greece says the pair treated her better than their biological children and that she loved them.
The brother of the man claiming to be Maria’s father repeated the defense that she had been given to them lawfully after her birth.
A lawyer representing the Roma couple, Kostas Katsavos, said they were carrying out a search for the girl’s mother.
Kostas Katsavos said the couple claim the woman had given Maria to them because she could not look after her own biological daughter.
“Our clients’ claim is that <<we never abducted this child we just adopted her>> in a way that was not legal, that we can confess,” said the lawyer.
But the couple are suspected by social workers of kidnapping the girl and sending her out to beg.
Police initially raided the Roma camp to search for drugs and weapons.
They noticed the lack of resemblance between the blonde-haired, green-eyed, pale-skinned little girl and her parents, and found further discrepancies when they investigated the family’s documents.
The couple had registered different numbers of children with different regional family registries.
The Greek authorities say the couple were in possession of false papers which suggested the woman had given birth to six children within a 10-month period.
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