Pochettino resigned his post as head coach at Southampton on Tuesday, leaving to take over at Premier League rivals Tottenham on a five-year deal.
The Argentinian led Southampton to an eighth-place finish last season, with the club earning praise for their attractive style of play.
And Le Tissier, who spent his entire professional career at Southampton from 1986 to 2002, has called on the Southampton hierarchy to pick a replacement with the same philosophy as Pochettino.
"Everything is in place there for a manager to make a success of things," Le Tissier told Sky Sports News.
"I think that is the most important thing; that we do find someone similar to Pochettino in the way he wants to play the game. The most important thing is that the new manager has the same philosophy that Mauricio had."
Murat Yakin, who left Swiss side Basel earlier this month, is the favourite for the job, while Ronald Koeman and Michael Laudrup are also thought to be in the running.
Le Tissier believes that the pedigree of coaches mentioned in connection to the job is testament to the progress Southampton have made in recent years.
"I think it shows how far the club has come in a short space of time," he added. "A few years ago you wouldn't have had the calibre of manager that are in the bookmakers odds.
"It bodes well and there is going to be a lot of candidates.
"There is plenty of work to be done and the sooner it gets done the sooner the club can work on their own transfer targets and strengthen our own squad."
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