We present a novel way of reusing the Krylov information generated by GMRES for solving the linear system arising within a Newton method. Our approach departs from the theory of secant preconditioners developed by Martinez and then combines secant updates of the Hessenberg matrix generated by the Arnoldi process in GMRES, the Richardsn iteration and limited memory quasi-Newton compact representations to generate descent directions for each Newton step. The proposed method allows to reflect - without explicitly computing them - secant updates of the Jacobian matrix that lead us to skip GMRES for the benefit of satisfying the Dembo-Eisenstat-Steihaug condition. Hence, the resulting method turns out to be computationally more economical than traditional inexact Newton implementations. Computational experiments reveal the suitability of this approach for large scale problems in several application contexts.