Given that the Bible is, and always has been, a very well preserved book, it's not a very good idea for a false religion to claim it is prophesied within. Ask any Muslim, as Muhammad actually tried to claim he is mentioned in the Bible (Qur'an 7:157). They'll tell you it makes a religion extremely difficult to defend the moment you try to use the Bible as your defence.
But Jesus had an advantage. He didn't have to claim He was mentioned in a book that the general public couldn't read during His ministry. He didn't need Zakir Naik or Shabir Ally to try to crowbar his name into Song of Solomon. He didn't need Joseph Smith to write an extra few verses to the end of Genesis and call it a "translation". Unlike the (not surprisingly few) false prophets who merely claimed the Bible mentions them, the entire Old Testament talks about Jesus.
That's why the New Testament doesn't just have the occasional "you'll find Him in the Tanakh, go look." Rather, it is able to repeatedly say "thus it was fulfilled which was spoken by the prophets...", and follow it up with exactly what the prophets said. In fact, a significant portion of the New Testament could be described as a re-cap of the Old, and a perfect picture of the fulfillment thereof.
This should really show us how different Christianity is from every other faith in the world. No other faith has a 100% success rate with prophecy. No other prophet fulfills such a wide variety of Old Testament prophecies. Even modern Judaism, despite having the correct Old Testament, is a failure, because if Jesus is not the Messiah, there is no Messiah. And yet our faith, the Christian faith, was foretold, piece by piece, starting from the moment man fell (Genesis 3:15). What an awesome God we have, who declares the end from the beginning (Isaiah 46:10), not just because He can do so in His omniscience, but because He actually loves us enough to leave our ancestors with hope, and us with proof that their hope was not misplaced. God's grace knows no boundaries.