It is not possible, at present for the Jewish State of Israel to build anything on the Temple mount.
The other problem is that the area now known as "The Temple Mount" is actually the location of Fort Antonia.
The Jewish historian Josephus said Fort Antonia was built upon a gigantic rock.
That rock is now under the Dome of the Rock.
The location of the Jewish temple was near Gihon Spring.
Mat 24:1 And Jesus went out, and departed from the temple: and his disciples came to him for to shew him the buildings of the temple.
Mat 24:2 And Jesus said unto them, See ye not all these things? verily I say unto you,
There shall not be left here one stone upon another, that shall not be thrown down.
Luk 19:41 And when he was come near, he beheld the city, and wept over it,
Luk 19:42 Saying, If thou hadst known, even thou, at least in this thy day, the things which belong unto thy peace! but now they are hid from thine eyes.
Luk 19:43 For the days shall come upon thee, that thine enemies shall cast a trench about thee, and compass thee round, and keep thee in on every side,
Luk 19:44 And shall lay thee even with the ground, and thy children within thee;
and they shall not leave in thee one stone upon another; because thou knewest not the time of thy visitation.
Mar 15:16 Then the soldiers led Him away into the hall called
Praetorium, and they called together the whole garrison.
Act_23:35 he said, "I will hear you when your accusers also have come." And he commanded him to be kept in
Herod's Praetorium.
The following comes from Wars of the Jews, by Flavius Josephus, Book 5, Chapter 5, Section 8.
8. Now as to
the tower of Antonia, it was situated at the corner of two cloisters of the court of the temple; of that on the west, and that on the north;
it was erected upon a rock of fifty cubits in height, and was on a great precipice; it was the work of king Herod, wherein he demonstrated his natural magnanimity. In the first place, the rock itself was covered over with smooth pieces of stone, from its foundation, both for ornament, and that any one who would either try to get up or to go down it might not be able to hold his feet upon it. Next to this, and before you come to the edifice of the tower itself, there was a wall three cubits high; but within that wall all the space of the tower of Antonia itself was built upon, to the height of forty cubits. The inward parts had the largeness and form of a palace, it being parted into all kinds of rooms and other conveniences, such as courts, and places for bathing, and broad spaces for camps; insomuch that, by having all conveniences that cities wanted, it might seem to be composed of several cities, but by its magnificence it seemed a palace. And as the entire structure resembled that of a tower, it contained also four other distinct towers at its four corners; whereof the others were but fifty cubits high; whereas that which lay upon the southeast corner was seventy cubits high, that from thence the whole temple might be viewed; but on the corner where it joined to the two cloisters of the temple, it had passages down to them both, through which the guard (for there always lay in this tower a Roman legion) went several ways among the cloisters, with their arms, on the Jewish festivals, in order to watch the people, that they might not there attempt to make any innovations; for the temple was a fortress that guarded the city, as was the tower of Antonia a guard to the temple; and in that tower were the guards of those three (14). There was also a peculiar fortress belonging to the upper city, which was Herod’s palace; but for the hill Bezetha, it was divided from the tower Antonia, as we have already told you; and as that hill on which the tower of Antonia stood was the highest of these three, so did it adjoin to the new city, and was the only place that hindered the sight of the temple on the north. And this shall suffice at present to have spoken about the city and the walls about it, because I have proposed to myself to make a more accurate description of it elsewhere.
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