Fluorescence resonance energy transfer (FRET) between excited fluorescent donor and acceptor molecules occurs via the Förster mechanism over a range of 1-10 nm. Because of the strong (sixth power) distance dependence of the signal, FRET has been used to assess the proximity of molecules in biological systems. We used a scanning near-field optical microscope (SNOM) operated in the shared-aperture mode using uncoated glass fibre tips to detect FRET between dye molecules embedded in polyvinyl alcohol films and bound to cell surfaces. FRET was detected by selective photobleaching of donor and acceptor fluorophores. We also present preliminary results on pixel-by-pixel energy transfer efficiency measurements using SNOM.