The France ace was linked with a move away from the south coast last summer but was convinced to stay put.
However, the 25-year-old is ready to quit if Ronald Koeman's side can't break into the top four.
"In August, I wanted to take a move but the club had lost too many players to agree to sell me,” he is quoted as saying in French newspaper L'Equipe.
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Morgan Schneiderlin
"Since then I have had discussions with the leaders and I want to play at the highest level: it is important at 25 years old to finally know the Champions League.
"Given that, late in the season, Southampton may qualify for the Champions League and I can stay, who knows.
"I have no desire to be in front of my TV on Tuesday and Wednesday."
Schneiderlin signed for Saints in 2008 and has played 26 times this season.
The France international is valued at around £16m.
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