In light of the recent European developments in ion beam therapy, there is a strong interest from the biomedical research community to have more access to clinically relevant beams. Beamtime for pre-clinical studies is currently very limited and a new dedicated facility would allow extensive research into the radiobiological mechanisms of ion beam radiation and the development of more refined techniques of dosimetry and imaging. This basic research would support the current clinical efforts of the new treatment centres in Europe (for example HIT, CNAO and MedAustron). This paper presents first investigations on the feasibility of an experimental biomedical facility based on the CERN Low Energy Ion Ring LEIR accelerator. Such a new facility could provide beams of light ions (from protons to neon ions) in a collaborative and cost-effective way, since it would rely partly on CERN's competences and infrastructure. The main technical challenges linked to the implementation of a slow extraction scheme for LEIR and to the design of the experimental beamlines are described and first solutions presented. These include introducing new extraction septa into one of the straight sections of the synchrotron, changing the power supply configuration of the magnets, and designing a new horizontal beamline suitable for clinical beam energies, and a low-energy vertical beamline for particular radiobiological experiments.