For a closed orientable surface $S$, any map $f:S\! \ra\! S$ whose $n$-th power is homotopic to the identity, is homotopic to a homeomorphism $g$ of $S$ of order $n$. This famous theorem of Nielsen is known to fail in general for aspherical manifolds. In this paper, for model aspherical manifolds $M$ associated to a finitely extendable set of data, we, however, present a weaker version of Nielsen's result. We show that any homotopically periodic self-map $f$ of $M$ is homotopic to a fiber preserving homeomorphism $g$ of $M$ of finite order (but the order of $g$ is not necessarily equal to the homotopy period of $f$).