We assume that R is an associative ring with unity, M is an unital right R-Module and S=End(M). A module M is called (quasi-) Baer if the right annihilator of a (two-sided) left ideal of S is a direct summand of M.We show that a direct summand of a (quasi-) Baer module inherits the property and every finitely generated abelian group is Baer exactly if it is semisimple or torsion-free. We prove that an arbitrary direct sum of mutually subisomorphic quasi-Baer modules is quasi-Baer. We also show that the endomorphism ring of a (quasi-) Baer module is a (quasi-) Baer ring, while the converse is not true in general.