Old Testament prophecy only pointed to where Jesus was born, not to where He subsequently lived, but it did note that He would be a Nazarene. And, as Luke says, after the purification ritual they returned to Nazareth, which is where Mary and Joseph came from to be counted in the census in Bethlehem. “Luke 2:39 When Joseph and Mary had done everything required by the Law of the Lord, they returned to Galilee to their own town of Nazareth.” As I noted, that was within 40 days of Jesus’ birth. Herod questioned the Magi and learned from them the approximate date of Jesus’ birth, which the Magi told him was about two years ago. “Matthew 2:16 When Herod realized that he had been outwitted by the Magi, he was furious, and he gave orders to kill all the boys in Bethlehem and its vicinity who were two years old and under, in accordance with the time he had learned from the Magi.” Here you have to use reason: If the Magi told Herod that the child had been born about 2 years previously, then they could not possibly have subsequently visited the child in Bethlehem because Jesus was no longer there. Since scripture clearly says that after the purification rituals, Mary and Joseph returned to Nazareth, then the only possible place the Magi could have visited Mary and Joseph was in Nazareth. They followed the star to where the child was, not where He had been born.
It would seem this way; but I'm also interested in what the Scripture DOESN't say; namely that they were CURRENTLY in Nazareth when the Magi visited the HOUSE.
While it is highly likely; the facts, as we know them, do not permit me to state, with 100% assurance.
Matthew ends the verse arguing that Jesus' life in Nazareth fulfilled a messianic prophecy, which he quotes: "He will be called a Nazarene." However, no such prophecy is found in the Old Testament, or any other extant source.
Matthew 2:23