The French international midfielder has been in fine form for the Saints as the club have made a superb start to the English Premiership season.
Southampton are currently second on the table after winning eight of their 11 league games this season but will play their remaining games with the threat of Schneiderlin's departure hanging over their heads.
Schneiderlin told French daily newspaper, L'Equipe,: "If someone had told me at the end of the transfer window that Southampton would be second, I would not have believed it.
"A career passes quickly and I want to play for a big club.
"Today I am at Southampton, we are second in the Premier League, it's going well.
"We'll see at the end of the season if [a transfer] will happen. If we have qualified for the Champions League, I will make the choice."
Southampton manager Ronald Koeman refused to entertain several bids from Tottenham Hotspur in the summer while Arsenal are reportedly also interested in signing the influential midfielder.