Förster Resonance Energy Transfer (FRET) is a widely applied technique in biology to accurately measure intra-and inter-molecular interactions at the nanometre scale. FRET is based on near-field energy transfer from an excited donor to a ground state acceptor emitter. Photonic nanoantennas have been shown to modify the rate, efficiency and extent of FRET, a process that is highly dependent on the near-field gradient of the antenna field as felt by the emitters, and thus, on their relative distance. However, most of the experiments reported to date focus on fixed antennas where the emitters are either immobilized or diffusing in solution, so that the distance between the antenna and the emitters cannot be manipulated. Here, we use scanning photonic nanoantenna probes to directly modulate the FRET efficiency between individual FRET pairs with an unprecedented nanometric lateral precision of 2 nm on the antenna position. We find that the antenna acts as an independent acceptor element, competing with the FRET pair acceptor. We directly map the competition between FRET and donor-antenna transfer as a function of the relative position between the antenna and the FRET donor-acceptor pair. The experimental data are well-described by FDTD simulations, confirming that the modulation of FRET efficiency is due to the spatially dependent coupling of the single FRET pair to the photonic antenna.