This paper studies the possibility of direct extraction of the transversity and its accompanying T-odd parton distribution function (PDF) from Drell–Yan (DY) processes with unpolarized pion beam and with both unpolarized and transversely polarized proton targets. At present, such an extraction can be performed with the COMPASS experiment at CERN. The preliminary estimations performed for the COMPASS kinematic region demonstrate that it is quite realistic to extract both transversity and its accompanying T-odd PDF under COMPASS conditions.