Draxler, 19, signed a contract extension with the club in May to keep him at the Veltins Arena until 2018.
The Germany international has been linked with moves to the likes of Real Madrid and Borussia Dortmund, among others.
However, Draxler made it clear where his focus lies, outlining his goal to win trophies with Jens Keller's side.
"The aim to take one of three titles, I think that this team is ready for them," he told Bild.
"We are tightening a net to catch the teams (above Schalke)."
Schalke have not won the Bundesliga title since 1958, while rivals Dortmund have clinched the domestic crown in two of the last three seasons.
Draxler, though, is confident that Keller's men can overtake their neighbours in the near future.
"The last three years have been decisive for Dortmund," he added. "Before that Schalke were always ahead of them.
"Now we have reached the point where we again proceed slowly. The plan is, of course, to overtake them again and we are well positioned for this."
