NHS Greater Glasgow and Clyde (NHSGGC) informed families of the development via a closed Facebook group set up during a water contamination crisis.
The board confirmed it had received an update from the Crown Office.
But it added there was no indication prosecutors had "formed a final view".
Police Scotland launched a criminal investigation in 2021 into a number of deaths at the Queen Elizabeth University Hospital (QEUH) campus, including that of 10-year-old Milly Main.
The Crown Office and Procurator Fiscal Service (COPFS) instructed officers to investigate the deaths of Milly, two other children and 73-year-old Gail Armstrong.
Milly's mother previously told a separate public inquiry into the building of several Scottish hospitals that her child's death was "murder".
A review earlier found an infection which contributed to Milly's death was probably caused by the QEUH environment.
Prof John Cuddihy'sdaughter, Molly, contracted an infectionwhile being treated for cancer and later gave evidence at the Scottish Hospitals Inquiry.
The former senior detective described the corporate homicide investigation as "deeply troubling".
He told BBC Scotland News: "Whilst this is undoubtedly in the public interest, it further compounds the distress, anxiety and trauma experienced by our children, their families and indeed the staff who have cared for and continue to deliver outstanding clinical care for our children.
"Whilst our confidence in the ongoing public inquiry has been significantly eroded with theunexplained loss of key personnelwith whom families had developed trust, we must have faith in COPFS and indeed Police Scotland to carry out their investigations."
In a statement on Sunday, NHSGGC said: "Our sympathies remain with the families who have been affected by events at the Queen Elizabeth University Hospital and Royal Hospital for Children.
"We have received a communication from the Crown Office and Procurator Fiscal Service (COPFS) about this update to the status of their ongoing inquiry.
"It should be made clear that this letter does not indicate that the COPFS have formed a final view.
"They have thanked us for our voluntary contribution so far, and we will continue to co-operate with this investigation."
A Police Scotland spokesperson said: "COPFS asked Police Scotland to investigate a number of deaths at Queen Elizabeth University Hospital campus, Glasgow.
"Our investigation is ongoing, it would be inappropriate to comment further."
Scottish Labour Leader Anas Sarwar has campaigned on behalf of the families of the children who died.
He said it had taken four years to get to this stage and Milly's family could now be "one step closer" to getting justice.
Mr Sarwar added: "Throughout this entire ordeal, Kimberly and all those who lost loved ones have shown extraordinary courage, while the health board engaged in denial and cover-up.
"To this day, nobody has been held to account for what went so tragically wrong. I long argued that had this scandal occurred in the private sector, there would have been a criminal investigation.
"I hope the full force of the law is used so that no family ever again has to go through what Milly's family have been through."
Scotland's largest health board has been named as a suspect in a corporate homicide investigation following the deaths of four patients at a Glasgow hospital campus.