We analyze the transport properties of relativistic fluid composed of constituent quarks at finite temperature and density. We focus on the shear and bulk viscosities and study their behavior near chiral phase transition. We model the constituent quark interactions through the Nambu--Jona Lasinio Lagrangian. The transport coefficients are calculated within kinetic theory under relaxation time approximation including in--medium modification of quasi--particles dispersion relations. We quantify the influence of the order of chiral phase transition and the critical end point on dissipative phenomena in such a medium. Considering the changes of shear and bulk viscosities along the phase boundary we discuss their sensitivity to probe the existence of the critical end point.

10 pages, 10 figures