Unstable states of the η meson and the 3He nucleus predicted using the time delay method were found to be in agreement with a recent claim of η-mesic 3He states made by the TAPS collaboration. Here, we extend this method to a speculative study of the unstable states occurring in the ηd and η4He elastic scattering. The T-matrix for the η4He 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 the FRA. With an ηN scattering length, aηN = (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 aηN, namely, aηN = (0.28, 0.19) fm. The existence of an η4He unstable bound state close to threshold is hinted by aηN = (0.28, 0.19) fm, but is ruled out by large scattering lengths.