The gospel of John records several short conversations Jesus had as He began to attract disciples at the beginning His ministry. These conversations are contained in verse 35-51 of John 1.
One of John the Baptist’s disciples was Andrew. Two things led him to begin following Jesus. First, John proclaimed Jesus as “the Lamb of God.” Then, as Andrew heard Jesus speak, he became convinced that he had found “the Messiah.”
We do not have the words Jesus used that convinced Andrew that He was the anointed One. However, we do have words of Jesus available to us, that clearly show the truthfulness of Andrew’s conclusion.