In this paper, we present a general derivation of a modified fluctuation-dissipation theorem(MFDT) valid near an arbitrary non-stationary state for a system obeying Markoviandynamics. We show that the method for deriving modified fluctuation-dissipation theoremsnear non-equilibrium stationary states used by Prost et al (2009 Phys. Rev. Lett. 103090601) is generalizable to non-stationary states. This result follows from both standardlinear response theory and from a transient fluctuation theorem, analogous to theHatano–Sasa relation. We show that this modified fluctuation-dissipation theorem can beinterpreted at the trajectory level using the notion of stochastic trajectory entropy, in away which is similar to what has been done recently in the case of the MFDT nearnon-equilibrium steady states (NESS). We illustrate this framework with two solvableexamples: the first example corresponds to a Brownian particle in a harmonic trapsubjected to a quench of temperature and to a time-dependent stiffness; the secondexample is a classic model of coarsening systems, namely the 1D Ising model with Glauberdynamics.