Jesus never claimed to be the Living Water. He said, “Whoever drinks the water I give him will never thirst. Indeed, the water I give him will become in him a spring of water welling up to eternal life” (John 4:14). Jesus claimed to “give” living water, not to “be” living water. Here’s why:
Jesus said, “Whoever believes in me, as the Scripture has said, streams of living water will flow from within him” (John 7:38). Then John comments: “By this [living water] he [Jesus] meant the Spirit, whom those who believed in him were later to receive” (John 7:39a).
While Jesus does not identity who the “living water” is in John 4 (only that he “gives” it), a few chapters later the “living water” is identified as the “Holy Spirit.” You never see Jesus saying, “I am the Living Water.” But you do see Jesus saying, “When the Counselor [the Holy Spirit] comes, whom I will send to you from the Father, the Spirit of truth who goes out from the Father, he will testify about me” (John 15:26). Jesus claimed to be the dispenser of the Spirit of truth, the “living water” of John 4.
So if someone asks you, “What is the Living Water of John 4,” don’t say, “Jesus.” Say, “the Holy Spirit.” Because John 7:38-39 says so.