In this paper we estimate the double parton scattering (DPS) contribution for the heavy quark production in $pA$ collisions at the LHC. The cross sections for the charm and bottom production are estimated using the dipole approach and taking into account the saturation effects, which are important for high energies and for the scattering with a large nucleus. We compare the DPS contribution with the single parton scattering one and demonstrate that in the case of charm production both are similar in the kinematical range probed by the LHC. Predictions for the rapidity range analysed by the LHCb Collaboration are also presented. Our results indicate that the study of the DPS contribution for the heavy quark production in $pPb$ collisions at the LHC is feasible and can be useful to probe the main assumptions of the approach.
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