Now Schneiderlin, who is currently on World Cup duty with Les Bleus, has fuelled the speculation by admitting that he has ambitions to play Champions League football.
"I've been there [Southampton] for a long time now. We'll see how things go, but the directors know my position and what my intentions are," he told reporters.
"Everyone has ambitions, everyone has his own future in his hands, so we'll see. Every player wants to play on big occasions."
The 24-year-old is contracted to the South Coast club until 2017.