Context. The INTEGRAL satellite has been observing the γ-ray sky for 15 years and has detected over 900 X-ray sources of various nature. However, more than 200 of these sources still lack precise identification.Aims. Our goal is to reveal the nature of the high-energy sources detected by INTEGRAL. In particular, we want to improve the census of X-ray binaries.Methods. Photometry and spectroscopy were performed in July 2012 on 14 INTEGRAL sources in near-infrared at the Very Large Telescope on the European Southern Observatory-UT3 telescope equipped with the ISAAC spectrograph. We used Ks images reaching to a depth of magnitude 18.5 to look for unique counterparts to high-energy detections to check for both extended sources and photometric variability. The analysis of near-infrared spectral features allows us to constrain the nature of these X-ray sources by comparing them to stellar spectra atlases.Results. We present photometric and/or spectroscopic data for 14 sources (IGR J00465–4005, IGR J10447–6027, IGR J12489–6243, IGR J13020–6359, IGR J13186–6257, IGR J15293–5609, IGR J17200–3116, IGR J17404–3655, IGR J17586–2129, IGR J17597–2201, IGR J18457+0244, IGR J18532+0416, IGR J19308+0530, and IGR J19378–0617). We conclude that 5 of these are active galactic nuclei, 5 are cataclysmic variables, 2 are low- or intermediate-mass X-ray binaries, and 2 are Be high-mass X-ray binaries.Key words: infrared: stars / X-rays: binaries / binaries: general⋆ Based on observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 089.D-0181(A).