Small ground-based telescopes can effectively be used to look for transiting rocky planets around nearby low-mass M stars, as recently demonstrated for example by the MEarth project. Since December 2009 at the Astronomical Observatory of the Autonomous Region of Aosta Valley (OAVdA) we are monitoring photometrically a sample of red dwarfs with accurate parallax measurements. The primary goal of this ‘pilot study’ is the characterization of the photometric microvariability of each target over a typical period of approximately 2 months. This is the preparatory step to long-term survey with an array of identical small telescopes, with kick-off in early 2011. Here we discuss the present status of the study, describing the stellar sample, and presenting the most interesting results obtained so far, including the aggressive data analysis devoted to the characterization of the variability properties of the sample and the search for transit-like signals.