We extend the method of time delay proposed by Eisenbud and Wigner, to search for unstable states formed by η mesons and the 3He nucleus. Using few-body equations to describe η3He elastic scattering, we predict resonances and unstable bound states within different models of the η–N interaction. The η3He states predicted within this novel approach are in agreement with the recent claim of the evidence of η-mesic 3He made by the TAPS Collaboration.