In the framework of the baryogenesis via leptogenesis mechanism we study the link between the amount of baryon asymmetry and neutrino mass matrices. In particular, neglecting phases, we find that if the Dirac neutrino mass matrix is related to the up quark mass matrix, the baryon asymmetry is about three orders smaller than the required value. If the Dirac neutrino mass matrix is related to the down quark or the charged lepton mass matrix, the baryon asymmetry is about two orders smaller than the required value. In order to get a sufficient amount of baryon asymmetry we need a more moderate hierarchy in the Dirac neutrino mass matrix.

11 pages, RevTex. Comment added