Spectral energy distribution and its variability are basic tools for understanding the physical processes operating in active galactic nuclei (AGN). In this paper we report the results of a one-year near infra red (NIR) and optical monitoring of a sample of 22 AGN known to be gamma-ray emitters, aimed at discovering correlations between optical and gamma-ray emission. We observed our objects with the Rapid Eye Mount (REM) telescope in J, H, K, and R bands nearly twice every month during their visibility window and derived light curves and spectral indexes. We also analyzed the gamma-ray data from the Fermi gamma-ray Space Telescope, making weekly averages. Six sources were never detected during our monitoring, proving to be fainter than their historical Two micron all sky survey (2MASS) level. All of the sixteen detected sources showed marked flux density variability, while the spectral indexes remained unchanged within our sensitivity limits. Steeper sources showed, on average, a larger variability. From the NIR light curves we also computed a variability speed index for each detected source. Only one source (PKS 0208-512) underwent an NIR flare during our monitoring. Half of the sources showed a regular flux density trend on a one-year time scale, but do not show any other peculiar characteristic. The broadband spectral index alpha_ro appears to be a good proxy of the NIR spectral index only for BL Lac objects. No clear correlation between NIR and gamma-ray data is evident in our data, save for PKS 0537-441, PKS 0521-360, PKS 2155-304, and PKS 1424-418. The gamma-ray/NIR flux ratio showed a large spread, QSO being generally gamma-louder than BL Lac, with a marked correlation with the estimated peak frequency nu_peak of the synchrotron emission.

accepted for Astronomy and Astrophysics, 6 pages, 5 figures