Time Reversal Invariance Violating (TRIV) effects in neutron transmission through a nuclei target are discussed. We explore the possibility to search TRI violation using two important advantages of neutron nuclei interactions: the possibility of the enhancement of TRIV observables by many orders of magnitude, and the relatively large number of the nuclear targets, which provides the assurance of avoiding possible “accidental” cancelations of TRIV effects due to unknown structural factors related to the strong interactions. The absence of final state interactions for the set of specific observables makes these neutron experiments complementary to electric dipole moment (EDM) measurements. The comparison of expected results in neutron scattering at new high flux Spallation Neutron Sources with the existing limits on neutron, nuclear and atomic electric dipole moments (EDMs) shows that TRIV observables in neutron scattering can essentially improve the current limits on the TRIV interactions.