Goal exclusively revealed on January 11 that Arsene Wenger is plotting a January move for Draxler, while Schalke sporting director Horst Heldt insisted last week that the club are yet to receive a concrete offer.
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"It's looks unlikely that we will sign anyone. We are not close to anything," he told reporters.
"If something exceptional turns up of course we will do it."
Meanwhile, Wenger revealed that he is keen to tie captain Thomas Vermaelen down to longer terms.
The Belgian, whose current deal is set to expire in 2015, has struggled for minutes after falling behind Per Mertesacker and Laurent Koscielny in the pecking order - starting just three Premier League games.
He said: "I'm ready to extend Vermaelen's contract. He is a quality player and I'm open to it."