We study nonlocal vortex transport in mesoscopic amorphous Nb0.7Ge0.3 samples. A dc current I is passed through a wire connected via a perpendicular channel, of a length L=2�5 µm, with a pair of voltage probes where a nonlocal response Vnl[proportional]I is measured. The maximum of Rnl=Vnl/I for a given temperature occurs at an L-independent magnetic field and is proportional to 1/L. The results are interpreted in terms of the dissipative vortex motion along the channel driven by a remote current and can be understood in terms of a simple model.