They have several other children who have not been taken into care.
The youngster is said to be physically well and is due to be interviewed by specialist officers.
Unlike the case where a girl, known as Maria, was found in a gypsy settlement near Farsala in central Greece, DNA tests have yet to confirm that the couple she was found with are not her parents.
The only similarity is that the girl taken into care is a blonde-haired, blue-eyed child and had a different appearance from that of the couple she was living with.
In the Greek case, a DNA test on Maria proved she was not related to Christos Salis, 39, and Eleftheria Dimopoulou, 40, and the couple have been held on charges of abduction and document fraud.
Irish police are trying to establish the identity of the girl taken into care in Dublin and have contacted Europol and Interpol about missing children while investigations continue in Ireland.
It is understood that they may seek to take DNA samples from the parents and the child to fully determine whether they are her biological parents.
-AAP