The Premier League club had reportedly launched a bid for the 20-year-old at the beginning of the year.
Draxler has confirmed that he turned down the opportunity to join the Gunners.
"In January, there was an offer of Arsenal but I decided to stay. I will do same this summer. I want one more year in Schalke." he told BBC Sport.
Draxler is currently with the Germany squad at the World Cup in Brazil.