Suppose it is allowed for Jews in the present to build a Third Temple, does that temple have to stand on the Temple Mount? Modern Israel is in many ways (actually most) not similar to the Israelite's kingdoms. The laws and customs are very different, the territory controlled and so on. The kingdom is different, so could the temple, in the same way, be different?
Edit: With "allowed" I don't mean politically, I mean religiously. :) Some rabbis want to construct a Third Temple, which I understand. But I don't understand why they need it placed on the Temple Mount. This graphic of Herod's Temple, seem to indicate that the most important part of the temple (Holy Place) only encompassed a small part of the Temple Mount.