Unstable states of the eta meson and the 3 He nucleus predicted using the time delay method were found to be in agreement with a recent claim of η-mesic 3 He states made by the TAPS collaboration. Here, we extend this method to a speculative study of the unstable states occurring in the ηd and η 4 He elastic scattering. The T -matrix for η 4 He scattering is evaluated within the Finite Rank Approximation (FRA) of few body equations. For the evaluation of time delay in the ηd case, we use a parameterization of an existing Faddeev calculation and compare the results with those obtained from FRA. With an ηN scattering length, a ηN = (0.42, 0.34) fm, we find an ηd unstable bound state around −16 MeV, within the Faddeev calculation. A similar state within the FRA is found for a low value of a ηN , namely, a ηN = (0.28, 0.19) fm. The existence of an η 4 He unstable bound state close to threshold is hinted by a ηN = (0.28, 0.19) fm, but is ruled out by large scattering lengths.