We report on near-field optical spectroscopy based on the illumination of the sample with white light from a Xe arc lamp through a tapered optical fiber. The light transmitted through the sample is analyzed with a grating spectrometer in the spectral range between 400 and 750 nm. Our setup provides a unique possibility for recording detailed spectroscopic information within a short acquisition time. Near-field spectra acquired on gold clusters measuring 100 nm in diameter and 20 nm in height reveal a wavelength-dependent transmittivity with both reduced and enhanced light intensities probably stemming from surface plasmon excitation.