However, Le Tissier admitted that if a buyer were to come in with a world-record offer for Dutch centre-back, then the club would have to consider it.
He criticised Liverpool over their alleged illegal approach for Van Dijk, and all but ruled out the chance of Southampton selling the player to the Merseyside club.
"With what's gone on I think it would be certainly be highly unlikely, even if Virgil puts a transfer request in, that he'd go to Liverpool this summer," Le Tissier told talkSPORT.
"The club have no interest in selling Virgil this summer. He's got five years left on his contract and he's the captain of the club, and the club's intention is to keep him.
"But if a world record bid comes in, then of course every player has their price."
Liverpool formally apologised to Southampton over "any misunderstanding" and ended their interest in Van Dijk on 7 June after the south-coast club said they would report the Anfield club to the Premier League.
"I remember the days when Liverpool used to be quite classy in transfer negotiations," Le Tissier said.
"There have been no bids for Virgil this summer, and until a bid has been accepted you shouldn't be talking to the player."
He added: "There are probably only a handful of clubs in world football who are not a selling club if the price is right, and Southampton, unfortunately, are not one of them. You just have to live with that and get on with it."