  We rewrite the Tolman -- Oppenheimer -- Volkoff (TOV) equations for four and
higher dimensional static spherically symmetric stars so that they resemble the
equations for anisotropic cosmology. This becomes possible by treating the
curvature terms of the sphere as part of the matter sector. Comparing then with
the effective equations in the Loop Quantum Cosmology -- inspired models, we
propose analogous modifications to the TOV equations which contain one
arbitrary function. A linear function gives the TOV equations. If the function
and all its derivatives are finite then the solutions are non singular. For
$sin \; x \;$, an `image star' appears beyond the central region of maximal
pressures in the original star. This is evocative of a bouncing universe in
Loop Quantum Cosmology. We discuss possible observational consequences of these
features.
