Based on our Catholic Marian Liturgy, for example the Little Office of the Immaculate Conception or the Litany of Loreto,  the Ark of the Covenant is one of the titles of Our Lady. The Old Testament is full of prefigurements  of Our Lady.  The book "Mary Foreshadowed: or Considerations On the Types and Figures of Our Blessed Lady in the Old Testament" by Rev. F. Thaddeus 1885, gives the explanation of thirty one titles of Our Lady that come from the OT. Like the Ark which was made of incorruptible wood, Mary was "free from the corruption of sin..." . St. John Damascene calls her " the ark of the Living God ". Fr. Thaddeus spends pages on making the comparison. 

I do not think that it matters how hard the Jєωs and archeologists search for the Ark of the Covenant, they will not find it until they look in the right places! We could give them the location! We know where Our Lady is, who carried Our Lord in her most holy and virginal womb and we know where the Tabernacle is that houses Our Lord in a true Catholic Church. When they find the faith, they will find the "Ark of the Covenant".

If I ever hear that the physical Ark of the Covenant has been found, I will think it is a scam.  Maybe it is hidden because we no longer need it, as the fulfillment of the Old Testament is now found in Our Lord, and through His Church. 

It may be that an Ethiopian Orthodox monastery does have it, as is claimed.  It would be a holy relic like any such thing that could be recovered from Old Testament times, but it would have no theological significance for Catholics not.  As is correctly pointed out above, our Ark of the Covenant is the Theotokos.

Even if the Church owned the Ark of the Covenant as a relic.  The
Vatican 2 Popes would have given it to Israel to confirm the modern
heresy that the Jєωs do not need to Convert, and the old covenant
is still valid.
It is for the best that it stays hidden.

II Maccabees:

1 You shall also find it set down in the dispositions made by the prophet Jeremias, that he bade the exiles rescue the sacred fire, in the manner aforesaid. 2 Strict charge he gave them, the Lord’s commandments they should keep ever in mind, nor let false gods, all gold and silver and fine array, steal away their hearts; 3 with much else to confirm them in their regard for the law. 4 And here, in this same docuмent, the story was told, how a divine oracle came to Jeremias, and he must needs go out, with tabernacle and ark to bear him company, to the very mountain Moses climbed long ago, when he had sight of God’s domain. 5 A cave Jeremias found there, in which he set down tabernacle and ark and incense-altar, and stopped up the entrance behind him. 6 There were some that followed; no time they lost in coming up to mark the spot, but find it they could not. 7 He, when they told him of it, rebuked their eagerness; Nay, said he, the place must remain ever unknown, till the day when God brings his people together once more, and is reconciled; 8 then, divinely, the secret shall be made manifest. Then once again the Lord’s majesty shall be seen, and the cloud that enshrines it; the same vision that was granted to Moses, and to Solomon when he prayed that the great God would have his temple on earth; 9 Solomon, the master of wisdom, that in his wisdom offered sacrifice to hallow the temple he had made.

The mountain is called Mount Nebo. The Ark of the Covenant is still there, hidden.

Beat me to it. Thanks for the verse.