Jesus does not directly answer the woman’s question, but He certainly does indirectly.

Note the contrast with the preceding verse.  The verb tense for “drinks” is different; the first is present “everyone who drinks continually” and the second is aorist “whoever has drunk once for all.”  Also contrast the impermanency of the first with the permanency of the second.  The “whosoever”s are different words in the Greek.  Abbott thinks the contrast is between “the multitude of those who go wrong” and “the individual that goes right.” (qt’d in Morris p. 262)

Jesus says “never thirst” not because He gives a once and for all drink; but because the water He gives becomes an ever-flowing spring within us.  We will not thirst because our need will be met before it progresses to the point of our knowledge of it.

“whoever drinks” refers to those who are affected by the water Jesus gives.  Note that the only ones who will never thirst are those who drink of Jesus’ water.  Note also that this water is available to “whoever” which is born out by the fact that Jesus is telling this to a Samaritan woman.

“in him” indicates the location of this water is within the person who drinks of it.

Most men draw their supplies from without. They are happy or satisfied when they have possessions, health, fame, power, and when things go well for them. When they receive that which they desire, their thirst is satisfied for a while, but it quickly returns when things go badly. Even those things they gain, quickly lose their ability to satisfy (Ec 5:10), and they require an increasing amount to bring them their temporary happiness. As the old saying goes, “he who begins by carrying a calf, before long is able to carry an ox.” Lust satisfied demands more lust and more and more.

Ec 5:10  Whoever loves money never has money enough; whoever loves wealth is never satisfied with his income. This too is meaningless.

“well” tells of an abundant supply.  The water of which the person drinks will become a whole well within him, not just a full drinking glass.  The once-and-for-all small drink becomes an infinite supply.

“water” refers to the Holy Spirit (cf. John 7:38-39).  Jesus gives us the Holy Spirit, and He wells up within us to eternal life.  The Holy Spirit is the One Who actually produces this life but Jesus is the One Who gives Him and thus it.  The Holy Spirit becomes a constantly flowing well which continuously satisfies our thirst even as it arises.

John 7:38-39  Whoever believes in me, as the Scripture has said, streams of living water will flow from within him.” By this he meant the Spirit, whom those who believed in him were later to receive. Up to that time the Spirit had not been given, since Jesus had not yet been glorified.

“welling up” is the same word translated as the leaping of the formerly lame man in Acts 3:8.  The life which Jesus gives is not just a translation from one state of being (lost) into another (saved); it is energetic and alive and abundant; it is real life as it should be. We are no longer like the weeds in a river which are always pointed downstream because they can’t resist the current. Our life is one of power and choice. Circumstances no longer dictate our actions or our joy.

Acts 3:8  He jumped to his feet and began to walk. Then he went with them into the temple courts, walking and jumping, and praising God.

This has another application besides just blessing those who receive. This life is a life of action. Christians cannot lie around dormant, just soaking in blessings without producing Godly activity. The life we have within us springs into action within us and through us to touch others with God’s love.

All water seeks its own level, so most fountains rise and fall into a basin, but not this one. The fountain of everlasting life has a different level than all other fountains and is not affected by gravity. Its level is its Maker — Christ Himself. When we receive His living waters within us, they will rise up from one level to the next and on to the next until we one day stand in His presence, having been made into His likeness by His Spirit (2Co 3:18). What an incredible difference there is between the life which He gives and that of this temporal world!

2 Corinthians 3:18  And we, who with unveiled faces all reflect the Lord’s glory, are being transformed into his likeness with ever-increasing glory, which comes from the Lord, who is the Spirit.