  We investigate the relation between the \eta ^3He binding energy and width
and the (complex) \eta ^3He scattering length. Following our systematic
analysis of the eta 3He scattering length we set limits on the \eta ^3He
binding. If bound states exist the binding energy (width) should not exceed 5
MeV (10 MeV). In addition, we comment on a recently claimed observation of an
\eta-mesic ^3He quasi-bound state by the TAPS collaboration based on \eta
photoproduction data. Although our limits are in reasonable agreement with the
values reported by this collaboration, our analysis of these data does not lead
to a solid conclusion concerning the existence of an \eta-mesic bound state.
More dedicated experiments are necessary for further clarification.
