Earlier this month it was announced that French authorities were investigating the deaths of three babies at a hospital in Chambery, south east France, who all died on different days in December last year.
The deaths have been blamed on bacteria in a batch of IV nutrient bags that were given to the newborns while they were in the neonatal intensive care unit.
On Wednesday regional newspaper Le Dauphiné Libéré reported that hospital chiefs have alerted investigators to the suspect death of another baby on the ward in March 2013.
It is believed the newborn was given the same brand of nutrient bag linked to the deaths of the other three babies.
The deaths were linked to a “new” type of bacteria according to scientists who had studied the content of the bags.
Tests showed it was a "type of environmental enterobacteria that was unknown until now and has no name," said Jean-Claude Manuguerra from the Pasteur Institut.
Parents of the three babies have already filed criminal complaints for manslaughter against the hospital.
"We're lodged the complaint to find out what happened. There was a failure in the system and this failure needs to be found so it never happens again," said the 37-year-old father of one of the infants, who gave his first name as Laurent.
France's health minister, Marisol Touraine, then announced all the batch that included the affected IV bags had been withdrawn.
She called the deaths "an extremely grave accident".
The director of the hospital, Guy-Pierre Martin, previously told a news conference that the contaminated IV nutrient bags all came from a French pharmaceutical firm, but he refused to identify it, saying that was up to French government authorities.
He did not identify the lethal bacteria either.
He said the hospital would assume its responsibilities if the investigation found it liable.