The staff involved are employed by the North West Anglia Foundation Trust and provide non-medical services, such as cleaning, catering, portering and security.
According to a representative of the public service union Unison, the staff affected are “predominantly” based at Hinchingbrooke Hospital in Huntingdon.
A petition against any such change has been signed by more than 1,400 people.
After Unison brought the petition to Cambridgeshire County Council’s health committee on October 15, councillors committed to raising the issue with the NHS trust’s chief executive at their next meeting.
Part of the petition reads: “NHS staff were praised as heroes, but now North West Anglia Foundation Trust want to sell us off to a new private employer.
“In cleaning, catering, linen, patient services, porters, post room and security, we’ve been giving our all during the pandemic – and long before – but as thanks we face being thrown out of the NHS family.”
Unison regional organiser Cheryl Godber told the health committee: “These staff are concerned, very concerned, not just about their own future under a for-profit private contractor, but also for the future of the quality of services, particularly in the middle of an ongoing pandemic.”
In a statement, the chief operating officer for North West Anglia NHS Foundation Trust, Graham Wilde, said: “We are looking at tendering some of the services that we and our delivery partners are currently providing for soft facilities management services at Peterborough City, Hinchingbrooke and Stamford and Rutland Hospitals.
"This is to ensure that we are providing the best value for money for taxpayers while maintaining the high quality services that we and our patients expect.
“These services include the provision of cleaning, catering, portering, linen and security at both Hinchingbrooke Hospital and Stamford and Rutland Hospital, as well as cleaning and linen services within our staff accommodation buildings. The tender process will also include the current cleaning contract for the Robert Horrell Macmillan Centre and off-site Health Records facilities for Peterborough City Hospital.
“In addition to this we are also looking to tender grounds, gardens and pest control services, which will provide services to each of our three main sites.
“We are now working with approximately 70 trust staff affected by this process and the existing providers and we will be holding regular staff briefing sessions to keep them updated. We are also meeting regularly with representatives from Unite and Unison to discuss any concerns they may have and to ensure that they are aware of the timetable and approach being taken.”