Using $dV/dr = -E$ it is mathematically possible to prove that there exists a point in space where gravitational potential is zero but field is not.
But what is the physical feasibility of the above situation. Also given the fact that negative mass is not possible, is there a point in the real universe satisfying the given condition?
A potential for a given force field is only ever unique up to an additive constant $c$ (because $\nabla c = 0$ does not affect the force). Thus in a given force and potential choose a point with nonzero force, evaluate the potential at that point and use the resulting value to subtract it from the potential. Voilà.
If you say that you don't want to modify the potential and take it as given: Bad luck, there exist potentials that are nonzero everywhere, like the potential of a point mass ($\sim \frac{1}{r}$). In that case you won't find such a point you are looking for.
