  In this Letter we have proposed a point particle model that generates a
noncommutative three-space, with the coordinate brackets being Lie algebraic in
nature, in particular isomorphic to the angular momentum algebra. The work is
in the spirit of our earlier works in this connection,
  {\it {i.e.}} PLB 618 (2005)243 and PLB 623 (2005)251, where the $\kappa
$-Minkowski form of noncomutative spacetime was considered. This non-linear and
operatorial nature of the configuration space coordinate algebra can pose
problems regarding its quantization. This prompts us to embed the model in the
Batalin-Tyutin extended space where the equivalent model comprises of phase
space variables satisfying a canonical algebra. We also compare our present
model with the point particle model, previously proposed by us, in the context
of $\kappa$-Minkowski spacetime.
