The Frenchman, who is a rumoured target for Arsenal, has impressed for the south coast club this term and is looking forward to the next campaign under new manager Maurico Pochettino.
After a slow start under the Argentine, Southampton have lost just four times in 13 Premier League games, form which has seen them rise to a comfortable mid-table position.
|11/4||Southampton are 11/4 with Paddy Power to finish as the top promoted team
"Hopefully this season we can finish in the top 10 because that’s our target, and next year we can take another step, maybe to reach the top six.
"Maybe people will say there is no chance of us doing that - I am sure they will think that. I say to them: keep laughing. We will see who laughs last."
Reports have suggested that Schneiderlin is Arsenal boss Arsene Wenger's ideal replacement for the injury-prone Abou Diaby, but the midfielder remains focused on his duties on the south coast.
"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," he added.
"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."