[Commentary to the Book of Esther, pp. 23-24]
We do not know exactly where they are. Some say that they are in the Vatican. Others claim that they are in other places, but the truth is that they are buried somewhere under the Temple Mount. King Shlomo dug tunnels under the Temple Mount because he knew through his Divine Spirit that the Beit Ha-Mikdash would be destroyed.
Question: Isn't it written that Nebuchadnezar took everything (see Megillah 12a)?
Answer: The vessels which he took were replacement vessels. The original vessels are located under the Temple Mount.
Question: Aren’t there vessels in England that are associated with the Temple?
Answer: Perhaps, but the real ones are under the Temple Mount.
Question: The Menorah and the Table of the Show-Bread too?
Answer: Yes. As is known, Titus stole the Menorah. We see this in the Arch of Titus in Rome. The Jews of Rome have a custom to say Lamentations there on Tisha Be-Av. But those vessels were also replacements. There were ten Menorahs (Menachot 29a, 98b-99a) and many vessels. We do not know if he took the actual Menorah or a fake one which was placed in the Beit Ha-Mikdash to fool him into thinking that he plundered the Temple. Even if he took the actual Menorah, there are nine others. Nonetheless there is no need to search for them today. When the time comes, everything will be found, including the Ark of the Covenant and the jar of "Man" (Manna).
Question: Did anyone ever search for the vessels of the Beit Ha-Mikdash?
Answer: Many certainly searched, but they did not find them. There are different stories and fables.
Question: What about those people who claim to have seen the Ark?
Answer: Anything is possible. Nevertheless, everything that they saw also disappeared. Do not worry, there are others. Incidentally, my daughter who studies art made a relief of the Arch of Titus. She brought to my attention the fact that those who are walking in the relief are not walking in the direction of Yehudah to Rome, but the opposite: from Rome to Israel! And this is true today, too: we are all returning home!