In "Biblical Perspective" Randall McElwain writes:
Since the “living water” is the Holy Spirit given through the work of Jesus Christ, verse 38 may refer to “rivers of living water” flowing from Christ. Another possibility is that the “living water” represents the work of the Holy Spirit in the life of the believer. Because of that work, rivers shall flow to others, bringing them to Christ. Either way, Jesus is the source of the living water that springs forth in abundance far beyond the water used in the Feast of Tabernacles.
Discussion: What are the implications of this basic spiritual truth that Jesus is the source of living water?
Source: Jesus, Son of God: Adult Teacher's Insights, page 36.