In this paper, we investigate maximal subgroups of an almost subnormal subgroup $G$ in a division ring $D$ whose center is infinite. Among results, we prove that if $M$ is such a maximal subgroup, then $M$ is abelian provided $M$ is either locally finite or $FC$-group, and $D$ is weakly locally finite. Also, we prove a theorem on the existence of non-cyclic free subgroups of a maximal subgroup $M$ in such a $G$.