The 23-year-old Frenchman, signed from Strasbourg in 2008, says he wants to keep on improving and has effectively ruled out making a move abroad by setting his sights on a career in the Premier League.
"I am happy because I have improved in every way, but I know that I still have steps to progress," he said.
"This year I have had a good season, but next year I want to be even better. For me, next year is going to be the real thing.
"I want to prove myself to everyone again, and to get even better.
"In football, if you stop improving then you'll automatically go backwards."
Arsenal are reported to be ready to make a £10million summer move for Schneiderlin, who recently signed a new contract extension which ties him to Southampton until at least 2017.
The Frenchman added: "I am not going to lie and say that I am not happy that people are speaking about me and my games, but there is no point in me having a good season and then disappearing the year after.
"The main thing for me is to keep this going and to be able to be better in every game I play.
"I don't like to judge myself - that is down to other people - but I know that I have the capacity to play in the Premier League and I want to spend the rest of my life playing here."
Southampton last week