It is understood the couple allegedly bought the child in Bucharest from three Romanian traffickers, but the Foreign Office said it was not clear if the child's parents were involved in the deal.
The Britons were arrested last Wednesday by Romanian police on the Hungarian-Romanian border at Bors after a tip-off. They were trying to leave the country. Their car was searched and the child found hidden in a basket.
The Britons were taken to the police headquarters at Bucharest where they are being questioned, as are the three Romanians.
A Foreign Office spokesman said: 'The couple had negotiated to get this child through three Romanian mediators. They must have been running some sort of business.
'They sold this child - we don't know how much for. It appears somebody tipped the police off at the same time as the child was collected.'
The couple, who will not be named unless charged, have been forbidden to leave the country until police inquiries are completed. The baby has not been returned to her parents but placed in a Bucharest orphanage.Reuse content