Abstract: We analyze the data on cross sections and asymmetries for the pd -> eta He-3 reaction close to threshold and look for bound states of the eta He-3 system. Rather than parameterizing the scattering matrix, as is usually done, we develop a framework in which the eta He-3 optical potential is the key ingredient, and its strength, together with some production parameters, are fitted to the available experimental data. The relationship of the scattering matrix to the optical potential is established using the Bethe-Salpeter equation and the eta He-3 loop function incorporates the range of the interaction given by the empirical He-3 density. We find a local Breit-Wigner form of the eta He-3 amplitude T below threshold with a clear peak in vertical bar T vertical bar(2), which corresponds to an eta He-3 binding of about 0.3 MeV and a width of about 3 MeV. By fitting the potential we can also evaluate the eta He-3 scattering length, including its sign, thus resolving the ambiguity in the former analyses.