Jesus once asked his disciples who do people say he was.
They replied, “Some say John the Baptist [a first-century prophet, and a contemporary of Jesus]; others say Elijah; and still others, Jeremiah or one of the prophets.” But what about you?” he asked. “Who do you say I am?” Simon Peter answered, “You are the Messiah, the Son of the living God.” Jesus replied, “Blessed are you, Simon son of Jonah, for this was not revealed to you by man, but by my Father in heaven.” (Matthew 16:14-17)
When Jesus was speaking to the Samaritan woman, she said…
“I know that Messiah (called Christ) is coming. When he comes, he will explain everything to us.” Then Jesus declared, “I who speak to you am he.” (John 4:25-26)
Jesus even answered his critics directly when they asked him whether he was the Messiah.
“How long will You keep us in suspense? If You are the [Messiah], tell us plainly.” Jesus answered them, “I told you, and you do not believe…” (John 10:24-25)