Aims: The nearby galaxy clusters Abell 496 and Abell 85 are studied in the very high-energy (VHE, E > 100 GeV) band to investigate VHE cosmic rays (CRs) in this class of objects which are the largest gravitationally bound systems in the Universe. Methods: HESS, an array of four imaging atmospheric cherenkov telescopes (IACT), was used to observe the targets in the range of VHE gamma rays. Results: No significant gamma-ray signal is found at the respective position of the two clusters with several different source size assumptions for each target. In particular, emission regions corresponding to the high-density core, to the extension of the entire X-ray emission in these clusters, and to the very extended region where the accretion shock is expected are investigated. Upper limits are derived for the gamma-ray flux at energies E > 570 GeV for Abell 496 and E > 460 GeV for Abell 85. Conclusions: From the non-detection in VHE gamma rays, upper limits on the total energy of hadronic CRs in the clusters are calculated. If the cosmic-ray energy density follows the large-scale gas density profile, the limit on the fraction of energy in these non-thermal particles with respect to the total thermal energy of the intra-cluster medium (ICM) is 51% for Abell 496 and only 8% for Abell 85 due to its higher mass and higher gas density. These upper limits are compared with theoretical estimates. They predict about 10% of the thermal energy of the ICM in non-thermal particles. The observations presented here can constrain these predictions especially for the case of the Abell 85 cluster.