Officials representing Arsenal had flown out to Germany in order to negotiate a deal for the 20-year-old but were unwilling to match the £37.2 million valuation - also the players release clause - set by the Bundesliga side.
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“The fact is, [Schalke general manager] Horst Heldt had offers for me this winter,” Draxler told Sky Germany.
“I’m happy about that. On the other hand, it shows the respect I enjoy at this club, even if Heldt refuses without me being asked."
When asked if he would be moving this summer, Draxler replied: "I haven't thought that far.
“The next three months will be difficult, I want to play a better second half of the season with Schalke because I want to play for Germany at the World Cup. That's the main aim."
Having missed out on the midfielder, Arsenal are expected to reignite their interest in Draxler at the end of the season.
Schalke general manager Horst Heldt, who denied he had even held talks with Arsenal on January 30, claims the German club's refusal to sell Draxler was due to the club being unable to sign a replacement.
"There were offers for Julian this winter,” Heldt confirmed.
“We told him, but also that we wouldn't let him go.
“There was no replacement on the market and Julian didn't really want to leave. But he would have brought us a lot of money."
But Heldt concedes the club may not be able to keep Draxler beyond the end of the current campaign.
"The moment will come. We can't avoid this. He's an outstanding player in Europe - one day he'll leave us," he said.
Meanwhile, Arsenal's only signing of the January transfer window, Kim Kallstrom, who arrived on loan from Spartak Moscow on Friday, has been ruled out for six weeks after aggravating an existing back injury within the opening 30 minutes of his first training session on Saturday.