Context. We investigate the nature and the physical properties of ten z, Y, and J-dropout galaxies selected in the field of the lensing cluster A2667. Aims: This cluster is part of our project aimed at obtaining deep photometry at ~0.8-2.5 microns with ESO/VLT HAWK-I and FORS2 on a representative sample of lensing clusters extracted from our multi-wavelength combined surveys with Spitzer, HST, and Herschel. The goal is to identify a sample of redshift z ~ 7-10 candidates accessible to detailed spectroscopic studies. Methods: Our selection is performed using the usual dropout technique based on deep I, z, Y, J, H, and Ks-band images (AB ~ 26-27, 3σ), targeting z ≳ 7.5 galaxy candidates. We also include IRAC data between 3.6 and 8 μm, and MIPS 24 μm when available. In this paper, we concentrate on the complete Y and J-dropout sample among the sources detected with a high signal-to-noise ratio in both H and Ks bands, as well as the bright z-dropout sources fulfilling the color and magnitude selection criteria adopted by Capak and collaborators. SED-fitting and photometric redshifts were used to constrain the nature and the properties of these candidates. Results: Ten photometric candidates are selected within the ~7' × 7' HAWK-I field of view (~33 arcmin2 of effective area once corrected for contamination and lensing dilution at z ~ 7-10). All of these are detected in H and Ks bands in addition to J and/or IRAC 3.6 μm/4.5 μm images, with HAB ranging from 23.4 to 25.2, and have modest magnification factors between 1.1 and 1.4. Although best-fit photometric redshifts are obtained at high-z for all these candidates, the contamination by low-z interlopers is expected to be in the range ~50-75% based on previous studies, and on comparison with the blank-field WIRCAM Ultra-Deep Survey (WUDS). The same result is obtained when photometric redshifts are computed using a luminosity prior, allowing us to remove half of the original sample. Among the remaining galaxies, two additional sources could be identified as low-z interlopers based on a detection at 24 μm and the HST z850 band. These low-z interlopers are not accurately described by current spectral templates given the large break, and cannot be easily identified based on broad-band photometry in the optical and near-IR domains alone. A good fit at z ~ 1.7-3 is obtained when assuming a young stellar population together with a strong extinction. Given the estimated dust extinction and high SFRs, some of them could also be detected in the IR or sub-mm bands. Conclusions: After correction for contaminants, the observed number counts at z ≳ 7.5 seem to agree with expectations for an evolving LF, and be inconsistent with a constant LF since z ~ 4. At least one and up to three candidates in this sample are expected to be genuine high-z sources, although spectroscopy is still needed to confirm this. Based on observations collected at the European Southern Observatory, Paranal, Chile, as part of the ESO 082.A-0163.