The adverb already is in the emphatic position in the Greek sentence structure of this verse.

You have been made clean … by the teaching is literally “you (emphatic) are clean through the word.” New English Bible rendered “you have already been cleaned by the word.” Both Good News Translation and New English Bible express the agency of the Greek sentence (“through the word”) by the use of causative verbs (Good News Translation have been made clean; New English Bible “have … been cleansed”).

The passive expression in verse 3 may be transformed into an active one by rendering “What I have said to you has caused you to become clean already” or “My message to you has already caused you to become clean.”

Quoted with permission from Newman, Barclay M. and Nida, Eugene A. A Handbook on the Gospel of John. (UBS Handbook Series). New York: UBS, 1980. For this and other handbooks for translators see here .