A recent analysis of the Fermi Large Area Telescope data provided evidence for a high-intensity emission of high-energy gamma rays with a E^-2 spectrum from two large areas, spanning 50{\deg} above and below the Galactic centre (the 'Fermi bubbles'). A hadronic mechanism was proposed for this gamma-ray emission making the Fermi bubbles promising source candidates of high-energy neutrino emission. In this work Monte Carlo simulations regarding the detectability of high-energy neutrinos from the Fermi bubbles with the future multi-km^3 neutrino telescope KM3NeT in the Mediterranean Sea are presented. Under the hypothesis that the gamma-ray emission is completely due to hadronic processes, the results indicate that neutrinos from the bubbles could be discovered in about one year of operation, for a neutrino spectrum with a cutoff at 100 TeV and a detector with about 6 km^3 of instrumented volume. The effect of a possible lower cutoff is also considered.