Yes, the Talmud (Yoma 39b) does mention signs which prefigure the destruction of the Temple which it places forty years before the event.
Our Rabbis taught: During the last forty years before the destruction of the Temple the lot ‘For the Lord’] did not come up in the right hand; nor did the crimson-coloured strap become white; nor did the westernmost light shine; and the doors of the Hekal would open by themselves, until R. Johanan b. Zakkai rebuked them, saying: Hekal, Hekal, why wilt thou be the alarmer thyself? I know about thee that thou wilt be destroyed, for Zechariah ben Ido has already prophesied concerning thee: Open thy doors, O Lebanon, that the fire may devour thy cedars. (Zechariah 11:1)
As I mentioned earlier, Josephus reports similar omens, but he places them closer to AD 70 (War 6.288-99).
Thus were the miserable people persuaded by these deceivers, and such as belied God himself; while they did not attend nor give credit to the signs that were so evident, and did so plainly foretell their future desolation, but, like men infatuated, without either eyes to see or minds to consider, did not regard the denunciations that God made to them. Thus there was a star resembling a sword, which stood over the city, and a comet, that continued a whole year. Thus also before the Jews’ rebellion, and before those commotions which preceded the war, when the people were come in great crowds to the feast of unleavened bread, on the eighth day of the month Xanthicus, [Nisan,] and at the ninth hour of the night, so great a light shone round the altar and the holy house, that it appeared to be bright day time; which lasted for half an hour. This light seemed to be a good sign to the unskillful, but was so interpreted by the sacred scribes, as to portend those events that followed immediately upon it. At the same festival also, a heifer, as she was led by the high priest to be sacrificed, brought forth a lamb in the midst of the temple. Moreover, the eastern gate of the inner [court of the] temple, which was of brass, and vastly heavy, and had been with difficulty shut by twenty men, and rested upon a basis armed with iron, and had bolts fastened very deep into the firm floor, which was there made of one entire stone, was seen to be opened of its own accord about the sixth hour of the night. Now those that kept watch in the temple came hereupon running to the captain of the temple, and told him of it; who then came up thither, and not without great difficulty was able to shut the gate again. This also appeared to the vulgar to be a very happy prodigy, as if God did thereby open them the gate of happiness. But the men of learning understood it, that the security of their holy house was dissolved of its own accord, and that the gate was opened for the advantage of their enemies. So these publicly declared that the signal foreshowed the desolation that was coming upon them.
Besides these, a few days after that feast, on the one and twentieth day of the month Artemisius, [Iyar,] a certain prodigious and incredible phenomenon appeared: I suppose the account of it would seem to be a fable, were it not related by those that saw it, and were not the events that followed it of so considerable a nature as to deserve such signals; for, before sun-setting, chariots and troops of soldiers in their armor were seen running about among the clouds, and surrounding of cities. Moreover, at that feast which we call Pentecost, as the priests were going by night into the inner [court of the temple,] as their custom was, to perform their sacred ministrations, they said that, in the first place, they felt a quaking, and heard a great noise, and after that they heard a sound as of a great multitude, saying, “Let us remove hence.”
The thing is that, while it certainly is attractive to link the Talmud’s version with the event described in the gospels, first of all there is the dating problem. The Talmud was only codified and reached its final form around the 5th-6th century, or perhaps even as late as the 9th (that’s way too removed more than Josephus or the gospels from the events).