Yes, Saul knew of Jesus before his conversion.
The Apostle Paul, who was known as Saul before his conversion, was a well-known Pharisee who studied under Gamaliel, a famous Jewish rabbi and a leader in the Jewish Sanhedrin (Acts 2:33). The Pharisees heard of Jesus’ activities, and they came up with the plan to kill Jesus. We presume Saul would have heard of this plan.
In Paul’s letter to the Corinthians, he wrote something that might suggest he knew Jesus: 2 Corinthians 5:16, “Wherefore henceforth know we no man after the flesh: yea, though we have known Christ after the flesh, yet now henceforth know we him no more.”
On the road to Damascus, something so incredible happened that it changed the course of the Apostle Paul’s life, shaping the history of Christianity. By this time, the crucified and risen Jesus had appeared to several disciples. Saul, later called Paul, was a Pharisee – a Jewish leader, religious and educated in the Law.
He was zealous for God and sincerely believed that the Christian movement was dangerous to the Jewish faith. He thought he was serving God by persecuting and eliminating Christians.
He went to the high priest to request letters addressed to the synagogues in the city of Damascus. These letters asked for cooperation in arresting followers of Jesus, so Saul could bring them back to Jerusalem in chains.
Acts 9:3-6 (Life Application Study Bible, NLT) says, “As he was nearing Damascus on this mission, a brilliant light from heaven suddenly beamed down upon him! He fell to the ground and heard a voice saying to him, ‘Saul! Saul! Why are you persecuting me?’ ‘Who are you, sir?’ Saul asked. And the voice replied, ‘I am Jesus, the one you are persecuting! Now get up and go into the city, and you will be told what you are to do.’”
After Saul saw the supernatural light and heard the voice, he was convinced that Jesus had been resurrected from the dead. Saul was blind for three days after this miraculous experience, and he didn’t eat or drink anything. In a vision, Jesus spoke to a follower named Ananias, assigning him to go to Saul and restore his sight. Ananias told Saul that Jesus had sent him to get his sight back and be filled with the holy spirit, and when he laid his hands on Saul, instantly something like fish scales fell from his eyes, and he could see again. After this miracle, he was baptized. At first, the apostles didn’t trust him; they thought he was only pretending to be a believer!
When Barnabas told the other apostles how Saul had boldly preached the name of Jesus in Damascus, they accepted him, and he became the 12th Apostle of Jesus, replacing Judas.
The account of his conversion is told three times to three different audiences. See Acts 9:3-7 (to those hearing or reading the book of Acts), Acts 22:6-9 (to a Jewish mob who physically attacked Saul) and Acts 26:13-16 (to King Agrippa). Paul was not shy to admit the sinful mistakes of his past.