The 24-year-old midfielder said at a press conference ahead of France's last-16 encounter with Nigeria on Monday: "Listen, I'm aware of Southampton's situation.
"On a personal level, the club know my position and know what I want to do. I had a good conversation with all the directors.
"I've been there for a long time now. We'll see how things go, but the directors know my position and what my intentions are.
"Everyone has ambitions, everyone has his own future in his hands, so we'll see. Every player wants to play on big occasions."
Pressed further on whether he could follow former Southampton boss Mauricio Pochettino to White Hart Lane, Schneiderlin added: "I'm not saying anything."
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