Context: HgMn chemically peculiar stars are among the quietest stars of the main-sequence. However, according to theoretical predictions, these stars could have pulsations related to the high overabundance of iron peak elements, which are produced by atomic diffusion in upper layers. Such pulsations have never been detected from ground-based observations. Aims: Our aim is to search for signatures of pulsation in HgMn stars using the high quality lightcurves provided by the CoRoT satellite. Methods: We identified three faint stars (V>12), from a VLT-GIRAFFE multiobject spectrographic survey in a field planned for observation by CoRoT. They present the typical characteristics of HgMn stars. The three stars were observed by the CoRoT satellite during the long run (131 days) which started on 24 October 2007, with the exoplanets CCDs (Additional Programme). In the present work, we present the analysis of the ground-based spectra of these three stars and of the corresponding CoRoT lightcurves. Results: Two of these three HgMn candidates show low amplitude (less than 1.6 mmag) periodic variations (4.3 and 2.53 days respectively, with harmonics) which are compatible with periods predicted by theoretical models. The CoRoT space mission was developed and is operated by the French space agency CNES, with participation of ESA's RSSD and Science Programmes, Austria, Belgium, Brazil, Germany, and Spain.