One mights suggest that this idea that the Beit Hamikdash will begin its return to Jerusalem from its place in exile is alluded to in Maimonoide’s description of Moshiach: ”If he…built the Beit Hamikdash in its place…. he is definitely Moshiach.” Why are the words “in its place” necessary? And if they are necessary, why does Maimonides not name the place explicitly by saying, “if he… built the Beit Hamikdash in Jerusalem?”
The answer is that since, grammatically, “in its place” can also be read as “in his place,” it is an allusion to Moshiach’s place in exile* – that is, before he achieves the status of Moshiach vadai (Definite Moshiach). While still in exile, Moshiach builds a Small temple – a microcosm and a model of the Beit Hamikdash. This is a preparation for the future Beit Hamikdash. This Small Temple will be revealed first there, in exile, and will then return (with G-d and the Jewish people) to Jerusalem.
*On a simpler level, Moshiach's knowledge of the precise location of the Beit Hamikdash is one of the things that prove he is Moshiach Vadai (the Definite Moshiach). (See footnote in Likkutei Sichot, vol. 8, p. 362. See Also footnote in Likkutei Sichot, vol. 24, p. 652.)
From the book: Kuntres Beis Rabenu Shebebavel (The Holy temple In Transit) By the Lubavitcher Rebbe. Rabbi Menachem M. Schneerson. Translated by Rabbi Alexander Zushe Kohn.