The actual location of the Ark has been speculated on for centuries. According to both, the Mishna (the entire body of Jewish religious law that was passed down and developed before 200 CE, when it was finally redacted by Rabbi Yehuda HaNasi) and the Tanach (the Jewish scriptures which consist of three divisions–the Torah, the Prophets and the Writings), the Ark was hidden underneath the First Temple by King Solomon. More specifically, the sources point to a spot underneath what was called the Chamber of the Woodshed located in the Women’s Courtyard.
The same sources indicate that through prophesy, King Solomon foresaw the destruction of both Temples and the building of the Third, and last, Temple. He built a secret underground chamber for the Ark directly beneath the Holy of Holies (the inner sanctuary within the Temple that was said to retain some or all of its original sanctity for use in the future Third Temple) in accordance to the original blueprints of the Temple.
According to the Lubavitch Rebbe, (Menachem Mendel Schneerson, b. April 5, 1902- June 12, 1994, the spiritual leader of the enormous Chabad Lubavitch movement and one of the most prominent and respected Hassidic rabbis of the 20th century) we see from the above sources that the Ark isn’t just a vessel, but an integral spiritual part of the Temple and the Holy of Holies itself. Thus, the Ark is what transforms the Temple from a “mere” house of worship into an actual House of G-d. If the Holy of Holies and the Ark are found in their original location, it will prove an indisputable, unbroken connection between all three Temples.
It is also interesting to note the fashion in which the Ark was lowered from the Holy of Holies into its chamber. According to the Ralbag (Rabbi Levi ben Gershon, b.1288- d. 1344, one of the most respected medieval Jewish philosophers), and the Malbim (Rabbi Meir Leibush ben Jehiel Michel Weiser, b.1809- d.1879, a Russian Rabbi, preacher, and Bible commentator), the Ark was lowered to the chamber on a golden-tiled platform which was part of the floor of the Holy of Holies. This floor of was then re-tiled to hide the opening. This is significant on two counts. Firstly, it shows that when the Ark is found it will sit on part of the original floor of the Holy of Holies, once again demonstrating the intrinsic connection of the three Temples. Secondly, it shows that the platform was never meant to come back up the same way it went down. Some other exit must have been created for the Kohanim who took the Ark down to the chamber, and to provide access to the chamber in the future.