Saints prevented Schneiderlin from leaving last year in the wake of the summer exodus of star players.
But Saints legend Le Tissier does not expect the club to stand in Schneiderlin's way rivals come knocking.
Arsenal and Tottenham have both been linked with the France international, however, Le Tissier expects Schneiderlin to move to Manchester United instead.
“It’s probably more likely that he’ll leave than stay,” Le Tissier told Sky Sports.
“The big question is whether a top-four side meets his valuation.
“Out of those sides it is Manchester United that need him most as they still require strengthening in that position.
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Southampton legend Matt Le Tissier expects Morgan Schneiderlin to leave this summer
“Schneiderlin is the sort of player they should be looking for, having proven over the last few seasons that he can mix it with the top sides.
It’s probably more likely that he’ll leave than stay
Matt Le Tissier
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“It sounds like they’ve been looking at Schweinsteiger but if they don’t get him then Schneiderlin becomes their number one target.
“We paid about £1million for him back in 2008 so with a couple of promotions and another decent transfer fee it certainly represents another good return.
“I think Southampton have always been fair with players and not stood in their way when bigger clubs have met their valuation, which was shown last summer.
“Schneiderlin’s case last summer was under exceptional circumstances as so many players had already left.”