The teenager, linked with moves to Chelsea and Manchester United, has been urged to stay put by the former England international, who also feels that Ashley Cole is on the decline
As revealed by Goal, the Saints face a struggle to retain the 18-year-old's services, with the boyhood Chelsea fan keen to speak with the Blues over a possible transfer, while Manchester United is ready to make a 20 million pound bid in the summer.
The teenager looks set to decide his future at the end of the season and, while Le Saux is full of praise for Shaw's performances this term, he is convinced that the youngster is already in the right place to continue his development and improve further.
"I've been watching him play quite a lot," the former England international told Press Association Sport. "He has the qualities of an attacking fullback who has a lot of pace and a lot of energy [and] his defending is getting better as he gets more experienced.
"He's still very young and, the more experience he gains for his club and at Under-21s level, I feel that he's in the right place at the moment and his development is crucial."
Were Shaw to secure a move to Stamford Bridge, he would replace Ashley Cole, already usurped by Cesar Azpilicueta, and Le Saux believes that the veteran Chelsea fullback's performances have dipped recently, leaving his England place under threat.
"I would pick the player that is in form, playing regularly and deserves it on past performance for England," he continued.
"When you look at Ashley Cole, you think of the high standards he's set himself over his career and, when I've seen him play, he doesn't look as sharp as he had done before.
"Inevitably, after playing so many games and getting older, it does take a bit longer to recover from injuries and to maintain a level of fitness for that position, marauding forwards like he does.
"Maybe he's not able to play quite so many games.
"For Ashley Cole it's important he maintains his levels in training and when he plays. He's a fantastic professional, in terms of his attitude, and he has to maintain his focus."