Phase one of the project would see Abbey Pharmacy relocate from Howard Street, freeing up space ahead of redevelopment works at the Indoor Covered Market, due to begin in February 2026.
Phase two would involve refurbishing the rest of the three-storey building to accommodate GP and other health services, directly accessible to the public.
According to the Local Democracy Reporting Service, council officers have said they are already in talks with healthcare providers interested in occupying the space.
To pay for the works, the council proposes reallocating funds from the Pathfinder programme originally earmarked for a town centre music venue.
Around 拢1.3m would fund phase one, with a further 拢400,000 to support feasibility studies and detailed designs for the second phase.