Context : The radio source at the center of the cool-core galaxy cluster RBS 797 ( z=0.35 ) is known to exhibit a misalignment of its radio jets and lobes observed at different VLA scales , with the innermost \sim kpc-scale jets being almost orthogonal to the radio emission which extends for tens of kpc filling the X-ray cavities . Gitti et al . suggested that this peculiar radio morphology may indicate a recurrent activity of the central radio source , where the jet orientation is changing between the different outbursts due to the effects of supermassive binary black holes ( SMBBHs ) . Aims : We aim to reveal the nuclear radio properties of the brightest cluster galaxy ( BCG ) in RBS 797 and to investigate the presence of a SMBBH system in its center . Methods : We performed new high-resolution observations at 5 GHz with the European VLBI Network ( EVN ) on May 3 , 2013 , reaching an angular resolution of \sim 9 \times 5 mas ^ { 2 } and a sensitivity of 36 \mu Jy/beam . We also re-analyzed VLA archival data at 4.8 GHz in A- and B- configurations . Results : We report the EVN detection of two compact components in the BCG of RBS 797 , with a projected separation of \sim 77 pc . We can envisage two possible scenarios : the two components are two different nuclei in a close binary system , or they are the core and a knot of its jet . Both interpretations are consistent with the presence of SMBBHs . Our re-analysis of VLA archival data seems to favor the first scenario , as we detect two pairs of radio jets misaligned by \sim 90 degrees on the same \sim kpc scale emanating from the central radio core . If the two outbursts are almost contemporaneous , this is clear evidence of the presence of two active supermassive black holes whose radio nuclei are unresolved at VLA resolution . The nature of the double source detected by our EVN observations in the BCG of RBS 797 can be established only by future sensitive , multi-frequency VLBI observations . If confirmed , RBS 797 would be the first SMBBH system observed at medium-high redshift at VLBI resolution . Conclusions :