Electron beam cooling is examined as an option to reduce momentum of gold ions exiting the EBIS LINAC before injection into the booster. Electron beam parameters are based on experimental data (obtained at BNL) of electron beams extracted from a plasma cathode. Many issues, regarding a low energy high current electron beam that is needed for electron beam cooling to reduce momentum of gold ions exiting the EBIS LINAC before injection into the booster, were examined. Computations and some experimental data indicate that none of these issues is a show stopper. Preliminary calculations indicate that single pass cooling is feasible; momentum spread can be reduced by more than an order of magnitude in about one meter. Hence, this option cooling deserves further more serious considerations.