Former Cabinet minister Vince Cable, now leader of the Liberal Democrats, has called for the walk-in centre on Broad Lane to remain open.
The Sheffield Clinical Commissioning Group has revealed plans to close the facility and move its services to the Northern General Hospital, almost three miles away.
It has just finished running a consultation with members of the public on the proposed closure.
On a visit to the city to support Sheffield Hallam candidate Laura Gordon, who was recently selected to challenge Jared O’Mara for the seat at the next election, Cable spoke out against the proposed changes.