Lallana, who turns 26 at the end of next week, four years left on his contract and is being heavily linked with Manchester United, Liverpool and Tottenham.
Le Tissier said: “I desperately want Adam to stay. It’s been a pleasure to watch him play over the last few years, he’s the one guy I come to watch to entertain me.
“Each to their own and I wouldn’t blame him if he wants to go to a club that gives him Champions League football. “But if I could say anything to try and keep him at Southampton, it would be to remind him that he is the first name on the team sheet.
“Champions League clubs have bigger, stronger squads so he might not play as much if he leaves.
“And he is at a club on the up.
“Southampton could reach the Champions League one day. It’s going to be extremely difficult but if he and Luke Shaw both stay and they add to the squad they will give themselves a chance.
“Even then it will still be incredibly difficult, the seven teams above them are far more established and aren’t going to stand still so it might take a little time and quite a bit of investment.
“And a lot will obviously depend on whether the manager stays and who the club takes on if he doesn’t.
“There’s a lot up in the air at the moment. I know Les Reed has said there have been no bids for players and players aren’t going to be sold but every player has his price. “Look at Cristiano Ronaldo – his price was £80m and off he went. You can never say a player will not be leaving.”
Lallana’s future may also be determined by how he performs at the World Cup.
“He’s nailed on for a place in the squad and I would be disappointed if he didn’t start the first game, certainly his form warrants that,” continued Le Tissier.
“We can play a multitude of formations with the likes of [Daniel] Sturridge, [Raheem] Sterling, maybe Jack Wilshere and Alex Oxlade-Chamberlain. “But if Roy [Hodgson] plays with one up front Adam should be one of the three supporting players .
“He’s one of the best at that, he can play anywhere along that line - as the song goes, he can play on the left or the right!”
Matt Le Tissier was speaking at a Barclays Thank You Day event, where two amateur football teams were given the opportunity to play at Southampton's St Mary's Stadium by Barclays. This season Barclays is thanking fans, community heroes, players and managers for making the Barclays Premier League what it is. Join the conversation with #YouAreFootball.