The DAMA/LIBRA experiment shows 9.5σ evidence for an annual modulation in the (1 − 6) keV energy range, strongly suggesting that the observed modulation has the dark matter origin. However, the conventional interpretation in terms of WIMP-nucleon interaction is excluded by other experiments. We propose an alternative source of modulation in the form of neutrons, which have been liberated from surrounding material. Our computations are based on the so-called Axion Quark Nugget (AQN) dark matter model, which was originally invented long ago to explain the similarity between the dark and visible cosmological matter densities, i.e. Ω dark ∼ Ω visible . In our proposal the annual modulation is shown to be generated in keV energy range which is consistent with DL observation in (1 − 6) keV range. This keV energy scale in our proposal is mostly determined by spectral properties of the neutrinos emitted by the AQN dark matter particles, while the absence of the modulation with energies above 6 keV is explained by a sharp cutoff in the neutrino's energy spectrum at ∼ 15 MeV. This proposal can be directly tested by COSINE-100, ANAIS-112 and CYGNO experiments. It can be also tested by studying the correlations between the signals from these experiments and nearby axion search detectors.