The left-back has been linked with moves to Manchester United, Chelsea and Tottenham Hotspur during the summer. However, he will sign a new contract at St Mary's when he turns 18, according to The Sun.
The move has been backed by coach Mauricio Pochettino, who has insisted that he does not want to sell any of the club's star players.
The 41-year-old said: "We have total confidence in keeping all our valuable players.
"They believe in this project and want to stay here."
The England Under-17 international made 28 appearances for the Saints last season.