The 20-year-old was a player heavily linked with a switch to the Emirates Stadium, but a reported £25million deal failed to materialise.
Draxler confirmed to BBC Sport he intended to remain in the Bundesliga again next term.
"In January there was the offer of Arsenal, but I decided to stay. I will do the same this summer. I want to play one year more in Schalke," said Draxler.
Arsenal manager Arsene Wenger rejected the chance to sign back former captain Cesc Fabregas from Barcelona, with the midfielder instead joining Chelsea, but is expected to strengthen his squad after the World Cup.
The agent of Italy forward Mario Balotelli refused to play down talk of a potential switch from AC Milan for the former Manchester City man, while Spain international Santi Cazorla has been quoted as saying he would make a decision on his future when back from Brazil, amid interest from Atletico Madrid.
Arsenal captain Thomas Vermaelen has been linked with a £10million move to Manchester United, but Wenger is in need of defensive reinforcements following the departure of full-back Bacary Sagna to Manchester City on a free transfer.
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