The Messiah is largely based on Jewish tradition, but there are passages that are accepted by the majority as being messianic. Here is a list I compiled a while ago:
2 Shmuel 7:10-13 (Samuel)
And I will appoint a place for My people, for Israel, and I will plant them, and they will dwell in their own place, and be disturbed no more; and the wicked people shall not continue to afflict them as formerly.
And even from the day that I commanded judges to be over my people Israel; and I will give you rest from all your enemies. And the Lord has told you that the Lord will make for you a house.
When your days are finished and you shall lie with your forefathers, then I will raise up your seed that shall proceed from your body after you, and I will establish his kingdom.
He shall build a house for My name, and I will establish the throne of his kingdom forever.
This has not happened. Wicked people have been murdering Jewish people all throughout history. The Temple is not built. There is no King.
Yeshayahu 2-4 (Isaiah)
And it shall be at the end of the days, that the mountain of the Lord's house shall be firmly established at the top of the mountains, and it shall be raised above the hills, and all the nations shall stream to it.
And many peoples shall go, and they shall say, "Come, let us go up to the Lord's mount, to the house of the God of Jacob, and let Him teach us of His ways, and we will go in His paths," for out of Zion shall the Torah come forth, and the word of the Lord from Jerusalem.
And he shall judge between the nations and reprove many peoples, and they shall beat their swords into plowshares and their spears into pruning hooks; nation shall not lift the sword against nation, neither shall they learn war anymore.
People still go to war and the Temple has not been re-established.
Yeshayahu 11-12-13
And he shall raise a banner to the nations, and he shall gather the lost of Israel, and the scattered ones of Judah he shall gather from the four corners of the earth.
And the envy of Ephraim shall cease, and the adversaries of Judah shall be cut off; Ephraim shall not envy Judah, nor shall Judah vex Ephraim.
The lost tribes have not been gathered back to Israel.
Yeshahyahu 27-12-13
And it shall come to pass on that day, that the Lord shall gather from the flood of the river to the stream of Egypt, and you shall be gathered one by one, O children of Israel.
And it shall come to pass on that day, that a great shofar shall be sounded, and those lost in the land of Assyria and those exiled in the land of Egypt shall come and they shall prostrate themselves before the Lord on the holy mount in Jerusalem.
Not happened yet.
Yirmiyahu 31:33 (Jeremiah)
And no longer shall one teach his neighbour or [shall] one [teach] his brother, saying, "Know the Lord," for they shall all know Me from their smallest to their greatest, says the Lord, for I will forgive their iniquity and their sin I will no longer remember.
Nothing about needing a middle-man and we don't live in an age where everyone knows G-d is G-d.
Yechezkel 37:26-28 (Ezekiel)
And I will form a covenant of peace for them, an everlasting covenant shall be with them; and I will establish them and I will multiply them, and I will place My Sanctuary in their midst forever.
And My dwelling place shall be over them, and I will be to them for a God, and they shall be to Me as a people.
And the nations shall know that I am the Lord, Who sanctifies Israel, when My Sanctuary is in their midst forever.
Temple still not built and the Nations don't all recognise G-d as G-d.
Micah 4:1-3
And it shall be at the end of the days, that the mountain of the Lord's house shall be firmly established at the top of the mountains, and it shall be raised above the hills, and peoples shall stream upon it.
And many nations shall go, and they shall say, "Come, let us go up to the Lord's mount and to the house of the God of Jacob, and let Him teach us of His ways, and we will go in His paths," for out of Zion shall the Torah come forth, and the word of the Lord from Jerusalem.
And he shall judge between many peoples and reprove mighty nations afar off; and they shall beat their swords into plowshares, and their spears into pruning hooks; nations shall not lift the sword against nation; neither shall they learn war anymore.
People still go to war. L-rd's House not established.
Tzefanaiah 3:9-13 (Zefanaiah)
For then I will convert the peoples to a pure language that all of them call in the name of the Lord, to worship Him of one accord.
From the other side of the rivers of Cush, My supplicants, the community of My scattered ones-they shall bring Me an offering.
On that day you shall not be ashamed of all your deeds [with] which you rebelled against Me, for then I will remove from your midst those who rejoice in your pride, and you shall no longer continue to be haughty on My holy mount.
And I will leave over in your midst a humble and poor people, and they shall take shelter in the name of the Lord.
The remnant of Israel shall neither commit injustice nor speak lies; neither shall deceitful speech be found in their mouth, for they shall graze and lie down, with no one to cause them to shudder.
This hasn't happened either. None of it.
Zach 14:9-11
And the Lord shall become King over all the earth; on that day shall the Lord be one, and His name one.
The whole earth shall be changed to be like a plain, from the hill of Rimmon in the south of Jerusalem; but it [Jerusalem] will be elevated high and remain in its old place; from the gate of Benjamin to the place of the first gate, until the corner gate, and from the tower of Hananel until the king's wine-cellars.
And they shall dwell therein, and there shall be no more destruction; but Jerusalem shall dwell in safety.
Jerusalem is hardly dwelling in safety and polytheism is still a thing.
So Jesus did not gather the lost tribes, rebuild the temple, not a king etc.