The midfielder, who signed a deal in May to keep him at the Veltins Arena until the summer of 2018, is one of the hottest prospects in German football currently, which has seen him being linked with Real Madrid.
But it is the prospect of winning some silverware with Jens Keller's men which Draxler says fills him with a burning desire.
|33/1||Schalke are 33/1 with William Hill to win the Bundesliga
“We are tightening the net to catch the teams above us."
Draxler caused a stir last week when he admitted that he would fit nicely into club rivals Borussia Dortmund's midfield following interest shown by Jurgen Klopp's men this summer.
BVB have enjoyed a revival in recent years winning the Bundesliga twice in the last three seasons, and the teenage starlet is hoping Schalke can emulate their arch-rivals' recent success.
“The last three years have been decisive for Dortmund. Before that, Schalke were always ahead of them," he continued.
“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.”
Schalke won the DFB-Pokal in 2011, but last won the Uefa Cup in 1997 and have gone over 50 years since last winning the Bundesliga, back in 1958.
To help them mount a challenge this season they have recruited defender Felipe Santana from Dortmund, highly rated youngster Leon Goretzka from Bochum and Mainz striker Adam Szalai this summer.