After the identification of a candidate \gamma -ray transient in the error region of the binary black hole ( BBH ) merger GW150914 by the Fermi satellite , the question of whether BBH mergers can be associated to electromagnetic counterparts remains highly debated . Here , we present radio follow-up observations of GW170608 , a BBH merger that occurred during the second observing run ( O2 ) of the Advanced Laser Interferometer Gravitational-wave Observatory ( LIGO ) . Our radio follow up focused on a specific field contained in the GW170608 sky localization area , where a candidate high-energy transient was detected by the Fermi Large Area Telescope ( LAT ) . We make use of data collected at 1.4 GHz with the Karl G. Jansky Very Large Array ( VLA ) , as well as with the VLA Low-band Ionosphere and Transient Experiment ( VLITE ) . Our analysis is sensitive to potential radio afterglows with luminosity densities L _ { 1.4 GHz } \gtrsim 6 \times 10 ^ { 28 } erg s ^ { -1 } Hz ^ { -1 } . In the most optimistic theoretical models , \approx 20 \% of BBH events occurring in massive hosts could be associated with outflows as radio luminous as this . Although we find no evidence for the presence of a radio counterpart associated with the LAT candidate in the GW170608 error region , our analysis demonstrates the feasibility of future radio follow-up observations of well localized BBHs .