Le Saux, who played for both the Blues and Saints in his illustrious career, believes the 18-year-old left-back is at the right club to continue his development.
Shaw, a boyhood Chelsea fan, has been linked with a move to Stamford Bridge as long-term successor to Ashley Cole and is in line for a call up for England's friendly with Denmark next month.
Le Saux, an ambassador for the Budweiser Open Trials campaign, which will provide amateur footballers with the opportunity to play at Wembley in front of professional scouts, told Press Association Sport: "I've been watching him play quite a lot.
"He has the qualities of an attacking full-back who has a lot of pace and a lot of energy.
"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-21 level, I feel that he's in the right place at the moment and his development is crucial."
Cole's influence has waned and he is currently second-choice left-back for Chelsea and England.
Le Saux thinks it was inevitable age would impact on Cole, with the 33-year-old overtaken by Everton's Leighton Baines in the England pecking order.
"I would pick the player that is in form, playing regularly and deserves it on past performance for England," Le Saux added.
"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."
For Jose Mourinho's Chelsea, Cole's place has been taken by Cesar Azpilicueta, the Spain right-back playing on his 'wrong' flank.
A rib injury saw Cole drop out of the team initially and a poor performance at Newcastle on November 2 did not help matters.
He has started three Premier League games since, when Branislav Ivanovic was injured and Azpilicueta switched to right-back, and been an unused substitute in the last five games.
Mourinho insists Azpilicueta has been selected ahead of Cole purely on merit and that the England centurion has a future at Chelsea.
Le Saux, who is also an admirer of Aston Villa's on-loan Chelsea defender Ryan Bertrand and Kieran Gibbs of Arsenal, praised the Spaniard for his displays.
"Azpilicueta's done very well when he's played," he added.
"I have played right-back on occasion and it is difficult.
"It's comparable to driving a left-hand drive car in Europe. You have to recalibrate your brain a little bit. Thankfully there's no roundabouts on a football pitch."
:: The Budweiser Open Trials, in association with BT Sport, will see six regional trials take place across the country. The trials will culminate in a showpiece match at Wembley Stadium. Those who make the cut will have one last chance to prove it's never too late to achieve your dream as they play in front of professional scouts. Watch the first part of the Budweiser Open Trials on BT Sport on Saturday 8th March as part of its FA Cup coverage and subscribe to YouTube.com/BudweiserUK