No, it is not possible today. The technique to perform PGD exists, but performing it would cause such damage to the oocyte that it could not be inseminated later to create an embryo.
What can be done is PGD on the trophectoderm of embryos at the blastocyst stage, since this has about 200 cells distributed between two different structures: one is the inner cell mass (the part of the embryo that will develop into the future fetus) and the trophectoderm (the part of the embryo that will develop into the placenta and membranes).
Biopsy of 2-4 cells of the trophoectoderm does not significantly impair the potential and survival of the embryo and instead allows us to indirectly know the number of chromosomes of the egg.