Gravitational microlensing, when finite size source effects are relevant, provides a unique tool for the study of source star stellar atmospheres through an enhancement of a characteristic polarization signal. This is due to the differential magnification induced during the crossing of the source star. In this paper, we consider a specific set of reported highly magnified, both single and binary exoplanetary systems, microlensing events towards the Galactic bulge and evaluate the expected polarization signal. For this purpose, we consider several polarization models which apply to different types of source stars: hot, late type main sequence and cool giants. As a result we compute the polarization signal P, which goes up to P = 0.04 per cent for late-type stars and up to a few per cent for cool giants, depending on the underlying physical polarization processes and atmosphere model parameters. Given an I-band magnitude at a maximum magnification of about 12 and a typical duration of the polarization signal up to 1 d, we conclude that the currently available technology, in particular the polarimeter in FOcal Reducer and low dispersion Spectrograph 2 (FORS2) on the Very Large Telescope (VLT), potentially may allow the detection of such signals. This observational programme may take advantage of the currently available surveys plus follow-up strategy already routinely used for microlensing monitoring towards the Galactic bulge (aimed at the detection of exoplanets). In particular, this allows one to predict in advance for which events and at which exact time the observing resources may be focused to make intensive polarization measurements.