Turbophoresis is the migration of inertial particles towards the wall in a wall-bounded flow induced by turbulence. In this work, we analyze the effects of drag reducing polymer additives on turbophoresis in a turbulent channel flow. The numerical data set is obtained from a direct numerical simulation (DNS) of a turbulent channel flow of a viscoelastic fluid and laden with particles of different inertia. The results indicate that polymer additives decrease the turbophoretic drift. We establish that turbophoresis is reduced because of the smaller wall-normal variation of wall-normal fluid velocity fluctuations that occurs in all drag reducing flows. Hence a reduction of turbophoresis should be a common feature of all drag reducing flows such s fiber, bubble suspensions and MHD.