The Germany international forward was rumoured to be Arsenal's top transfer target in last transfer window, with manager Arsene Wenger thought to be a keen admirer.
However, the FA Cup winners' only January signing proved to be midfielder Kim Kallstrom, who joined on loan from Spartak Moscow.
Draxler has now stated that he had the opportunity to move to the Emirates Stadium, but the 20-year-old opted to remain in Gelsenkirchen.
"In January there was the offer of Arsenal, but I decided to stay," he told BBC Sport.
"I will do the same this summer. I want to play one year more in Schalke."
Draxler made 26 Bundesliga appearances last term, and contributed two goals as Schalke finished third in Germany's top flight.
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