It is beneath the structure on the Temple Mount. Both Hebrew temples we built on it and now the dome of the rock sit atop it.
Many people think that. There's another school of thought that believes the Temple was in the City of David; that the Temple required a source of running water (which does not exist on the "Temple Mount," but does exist at the Gihon Spring in the City of David) and that the "Temple Mount" was, in fact, the site of the Roman garrison in Jerusalem. The Romans could be very thorough when they wanted to utterly destroy something.