It is not possible at the moment. the furthest that we have drilled into the crust is a meagre 12km in the norilsk region of russia. the distance to the centre of the earth is approximately 6370km. the heat and friction cause melting very quickly. also the cost is enormous, billions of dollars. as the geology industry is largely militarily funded, there is no longer the investment in geology (end of cold war). also the inner core is solid, outer core liquid. no drill could be produced long enough either, so no.