  The goal of this article is to investigate nontrivial $m$-quasi-Einstein
manifolds globally conformal to an $n$-dimensional Euclidean space. By
considering such manifolds, whose conformal factors and potential functions are
invariant under the action of an $(n-1)$-dimensional translation group, we
provide a complete classification when $\lambda=0$ and $m\geq 1$ or $m=2-n.$
