We report on late time radio and X-ray observations of the tidal disruption event candidate ASASSN-14li, covering the first 1000 d of the decay phase. For the first ∼200  d the radio and X-ray emission fade in concert. This phase is better fitted by an exponential decay at X-ray wavelengths, while the radio emission is well described by either an exponential or the canonical t^−5/3 decay assumed for tidal disruption events. The correlation between radio and X-ray emission during this period can be fitted as . After 400 d the radio emission at 15.5 GHz has reached a plateau level of 244 ± 8 μJy which it maintains for at least the next 600 d, while the X-ray emission continues to fade exponentially. This steady level of radio emission is likely due to relic radio lobes from the weak AGN-like activity implied by historical radio observations. We note that while most existing models are based upon the evolution of ejecta which are decoupled from the central black hole, the radio–X-ray correlation during the declining phase is also consistent with core-jet emission coupled to a radiatively efficient accretion flow.