Can we use the mirror symmetry to define quantum gravity ?

It may be fair to say that so far we don't know how to quantize a Riemannian manifold (or a complex manifold). But a symplectic manifold may be more accessible for quantization because it endows a natural cosymplectic (Poisson) structure, e.g., for deformation quantization. If so, using the mirror symmetry, we may try to quantize a symplectic manifold instead of a complex manifold being mirror to the former. How can this approach for quantum gravity make sense ?