The Gunners were heavily linked with a swoop for the highly-rated Germany international in the mid-season window but a move failed to materialise.
And the playmaker, who scored five goals in 38 games last season, has revealed that he opted to reject the chance to move to Emirates Stadium in favour of staying in the Bundesliga.
“In January there was the offer of Arsenal, but I decided to stay,” Draxler told BBC Sport.
“I will do the same this summer. I want to play one year more in Schalke.”
Manchester United were also credited with an interest in signing Draxler back in January.
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