Sasha Ruseva and Atanas Rusev are said by Bulgarian media to have several children, some of whom resemble Maria.
The girl was reportedly born in Greece. But Sasha Ruseva is quoted as denying Maria was left there for money.
Bulgarian police have declined to comment on the reports.
Maria came to the Greek police’s attention after they raided the Roma camp near Farsala in central Greece, initially searching 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, Christos Salis and Eleftheria Dimopoulou, have since been charged with child abduction.
Maria is currently being cared for by a charity in Athens. There have been 8,000 inquiries following an appeal to identify her, and the international police body Interpol are involved in the search for her biological family.
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