The 24-year-old has been a reported target for Arsenal, while Serie A side Napoli are also understood to be keen.
Schneiderlin's form this season has been rewarded with a place in the seven-man contingency team for France's World Cup squad, and speaking at a Les Bleus press conference, he was coy on his future.
He said: "There is lots of speculation regarding my future. I still have another three years on my contract. The Champions League is my dream it is true.
"I cannot say that I want to leave out of respect for Southampton. I can adapt to all positions. I can sit in front of the defence or play box-to-box."
Southampton finished eighth in the Premier League last season.