In this proceedings article, we present the first steps towards the determination of the out-of-equilibrium conductivity of the Chiral Magnetic Effect (CME) in the presence of strong interactions. Using linear response theory, we obtain an analytical expression for the spectral function associated with this effect at one-loop in perturbation theory. In addition, we provide a first estimate of the CME conductivity by calculating the associated Euclidean correlator using quenched Wilson fermions and dynamical staggered fermions in physical Quantum Chromodynamics (QCD) simulations. In particular, we focus on the midpoint of the correlator, which can be used as a proxy of the full conductivity. We present results in a wide range of temperatures, showing how this observable is suppressed at low temperatures, while at high temperatures it approaches the perturbation theory prediction.