If the discussions are successful, Queen's Medical Centre, in Nottingham, will hold the contract to run the services at Grantham and Kesteven Hospital, Lincolnshire, from next April.
South Lincolnshire Health Authority commissioned an independent inquiry into the running of Grantham's paediatric ward in November last year, eight months after the deaths had occurred.
Earlier this year a former nurse at the hospital, Beverley Allitt, 23, was charged with the murder of four children between February and April 1991, and further accused of attempted murder and grievous bodily harm in respect of another nine children. She is also accused of two further counts of attempted murder and grievous bodily harm of two elderly patients.
The findings of the inquiry by a team from Trent Health Authority have been passed to South Lincolnshire which said it planned to release the details, but would do so after the criminal proceedings.
But the health service union, Cohse, yesterday demanded full disclosure and accused the management of sheltering behind a legal excuse in order to avoid publishing a report highlighting management mistakes.
Jenny Flood, one of the union's regional officers, said: 'This action by management serves no one's interests. It will do nothing to restore public confidence in local services or shattered staff morale.'
However, South Lincolnshire has said that a number of the recommendations regarding the running of the ward will be implemented at the hospital in the coming weeks. It also revealed that it had taken the highly unusual step of inviting Queen's Medical Centre to run paediatric services at the Grantham hospital in order to maintain the service in the area.
Sadie McIlroy, South Lincolnshire's director of public health, said: 'Queen's Medical Centre is a leading hospital with a deserved reputation for excellence. The health authority believes that it will provide the children of Grantham and surrounding areas with the highest standards of care.'