  We consider Nambu-Poisson 3-algebras on three dimensional manifolds $ {\cal
M}_{3} $, such as the Euclidean 3-space $R^{3}$, the 3-sphere $S^{3}$ as well
as the 3-torus $T^{3}$. We demonstrate that in the Clebsch-Monge gauge, the Lie
algebra of volume preserving diffeomorphisms $SDiff({\cal M}_{3})$ is identical
to the Nambu-Poisson algebra on ${\cal M}_{3}$. Moreover the fundamental
identity for the Nambu 3-bracket is just the commutation relation of $
SDiff({\cal M}_{3})$. We propose a quantization prescription for the
Nambu-Poisson algebra which provides us with the correct classical limit. As
such it possesses all of the expected classical properties constituting, in
effect, a concrete representation of Nambu-Lie 3-algebras.
