Let G/H be a contractible homogeneous Sasaki manifold. A compact locally homogeneous aspherical Sasaki manifold Γ\G/H is by definition a quotient of G/H by a discrete uniform subgroup Γ≤G
Nearby in the stack
. We show that a compact locally homogeneous aspherical Sasaki manifold is always quasi-regular, that is,
Γ\G/H
is an
S1
-Seifert bundle over a locally homogeneous aspherical Kähler orbifold. We discuss the structure of the isometry group
Isom(G/H)
for a Sasaki metric of
G/H
in relation with the pseudo-Hermitian group
Psh(G/H)
for the Sasaki structure of
G/H
. We show that a Sasaki Lie group
G
, when
Γ\G
is a compact locally homogeneous aspherical Sasaki manifold, is either the universal covering group of
SL(2,R)
or a modification of a Heisenberg nilpotent Lie group with its natural Sasaki structure. In addition, we classify all aspherical Sasaki homogeneous spaces for semisimple Lie groups.