Jobs could be lost at the Department of Work and Pensions (DWP) head office in Preston as part of a cost-cutting Government effort.
The DWP has announced that a Voluntary Exit Scheme is being run across the country, as it looks to slash 1,700 posts.
Which centres are affected will depend on the level of interest shown in the scheme after initial consultations.
It is possible, though unlikely, that all jobs could come from the same centre, with others unaffected.
A DWP spokesperson said: “We need to reduce costs in line with Government spending plans so have made operational decisions that will enable us to release some staff.
“We need to reduce our headcount by 1,700 people by the end of March 2017 and natural turnover of our staff will not yield this figure.
“That is why we are launching a small number of highly targeted Voluntary Exit Schemes in areas where in the future we know we will have more people than we need.
“These are the first steps of a Department-wide response to the challenges facing us now and to prepare us for what we know we will face in the future.”
The DWP said there had not yet been a discussion over the future of the Preston site, which is thought to employ around 750 people, because feedback from staff at the centre on the offer had not been received.
In June DWP staff who are part of the Public and Commercial Services Union (PCS) demonstrated in Lancaster Road, Preston.
Members were angry because they said 20,000 jobs have been cut in the DWP since May 2010, with “pensions attacked”, and years of pay restraint seeing members’ living standards drop by 20 per cent.