The deal is expected to include a £35million buy option and Alcaraz is keen to go.
The 21-year-old joined the Saints last January in a £12m deal from Racing Club and signed a four-and-a-half year deal.
He then went on to play 18 times in the Premier League as Southampton were relegated to the Championship.
Alcaraz has played 23 times in the Championship for Russell Martin's side, scoring three times. Just 13 of those appearances have been starts.
He also signed a contract extension as recently as October.
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His last league start for the club came on December 9, when he was taken off at half-time.
The Saints are currently third in the Championship, just one point behind second place Ipswich.
If Alcaraz completes the move to Juventus, he will go straight from a promotion fight to a title chase in Serie A.
Juve are just one point behind leaders Inter Milan, but they do have a game in hand.