The 20-year-old Germany international was a number one priority by the Gunners in January, but they plumped for a loan deal for Kim Kallstrom instead.
Draxler also attracted interest from Manchester United but a deal failed to materialise.
And it seems both Premier League clubs will have to put their interest in Draxler on hold following his latest comments.
“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.”
Draxler hit five goals in 38 appearances for the Bundesliga outfit last term.
Written by Steve Milne