The 24-year-old has had an impressive season for the Saints, playing his part in an expressive side that eventually finished eighth in the Premier League.
Alongside the England trio of Adam Lallana, Luke Shaw and Rickie Lambert, Schneiderlin has been one of the key players for Mauricio Pochettino's side, and his displays have seen him linked with the likes of the Gunners and Serie A giants Napoli.
The Frenchman has been rewarded for a fine campaign by being named in France's seven-man backup list for the World Cup, and speaking at a press conference for Les Bleus, he declined to refute rumours of a switch.
Rather than squash the transfer talk, the centre-midfielder admitted that playing in the Champions League was something he dreams about.
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."
Schneiderlin also revealed that his heroes are Liverpool captain Steven Gerrard and France legend Zinedine Zidane, but stopped short of comparing himself to either man.
"Zidane and Gerrard, they are my models, [but]I can adapt to all positions," he added. "I can sit in front of the defence or play box-to-box.
"It is not my mentality to wish for an injury on a player. I do not wish ill on anyone. Of course the next stage for me is Euro 2016. I am already thinking about it.”
Southampton could lose a number of their stars this term, with Lallana continually linked with a £20m move to Liverpool, while Manchester United and Chelsea are said to be keeping tabs on teenage left-back Shaw.