Hi!
I found this site to be interesting:
jewishvirtuallibrary.org/jsource/judaica/ejud_0002_0014_0_13744.html
One section of it states that it is thought that the messiah would be fully human. Therefore, I doubt that there is any exact phrasing in the Old Testament where God states explicitly that the messiah will be God the Son.
In rabbinic thought, the Messiah is the king who will redeem and rule Israel at the climax of human history and the instrument by which the kingdom of God will be established. While the Bible stresses the nature of the age called the “end of days,” the rabbis focus as well on the person of their regent, who gives the messianic age (yemot ha-mashi’aḥ) its very name. “Messiah” (Mashi’aḥ) means “anointed” and in the Bible can refer either to a king or a priest. The aggadah restricts the term to the eschatological king, who is also called malka meshiḥa (“king messiah”) in the Targums, ben David (“son of David”), and mashi’aḥ ben David (“Messiah, son of David”). The Messiah was expected to attain for Israel the idyllic blessings of the prophets; he was to defeat the enemies of Israel, restore the people to the Land, reconcile them with God, and introduce a period of spiritual and physical bliss. He was to be prophet, warrior, judge, king, and teacher of Torah…
The Messiah is generally assumed to be man, though writ large. As such, he can come either riding a donkey, in subdued fashion (cf. Zech. 9:9), or triumphantly riding the clouds (Dan. 7:13). **That the Messiah is fully human is dramatically shown by Akiva’s knowledgement of the rebel leader, Bar Kokhba, as the Messiah. **(Yet Akiva also declared that the Messiah would occupy a throne alongside God). One talmudic source does apparently attribute immortality to Messiah (Suk. 52a), and the Midrash (mostly later) singles him out among the immortals of Paradise. The Messiah does not displace either God or Torah in rabbinic thought. Thus, Hillel (fourth century) can deny the coming of Messiah (for which he is rebuked), though he doubtless expected Israel’s redemption. So too, the Midrash can declare that the ultimate author of redemption is not Messiah but God, and His kingship is stressed in the liturgy as well (Mid. Ps. to 31:1; 36:1; 107:1).
Peace