The 17-year-old is closing in on a move to Tottenham, but has also been linked with Manchester United and Arsenal.
Le Tissier said: “I would certainly like him to stay for at least one more season. I think as a young boy it’s important he has a good grounding in the game before he actually moves on.
“When you go to a big club, I think it’s proven with Theo Walcott, I think Theo moved a bit early and he has gone backwards a little since he’s been at Arsenal and I hope Gareth doesn’t do the same.
“Maybe another season in the Southampton side would do him a world of good before moving on.
“I’ve seen him play quite a bit now. I’ve been very impressed and going forward he’s one of the best left-backs I’ve seen. I think he will get better defensively when he gets older.
“I think he will be a top-class player and I think he will play for one of the big teams and I think he is destined for big things.”