The 23-year-old has impressed for the Saints this season, earning himself a four-year extension to his contract.
He was recently linked with a £10m move to Arsenal and said that he was happy to get recognition.
"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," Sky Sports News quotes the Frenchman as saying.
"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."
Schneiderlin arrived at St Mary's from Strasbourg in 2008.