  In this note, we study the normal compact K\"ahler (possibly singular)
threefold $X$ admitting the action of a free abelian group $G$ of maximal rank,
all the non-trivial elements of which are of positive entropy. If such $X$ is
further assumed to have only terminal singularities, then we prove that it is
either a rationally connected projective threefold or bimeromorphic to a
quasi-\'etale quotient of a complex $3$-torus.
