No- if you think about a 'classical' particle (that is, ignore quantum effects), once you are inside the particle the gravitational pull is proportional to the distance from the center.

In other words, if you are outside a spherical mass the pull of gravity gets stronger as you get closer (~1/r^2). But once you are inside the mass, the pull gets weaker. Hence there is no black hole at the center of the earth, for example.