It was thought that Wenger was plotting a January move for Draxler, while Schalke sporting director Horst Heldt insisted last week that the club has yet to receive a concrete offer.
Arsenal has also been linked with recognized striker talents following injuries to the likes of Theo Walcott, though Wenger ruled out a bid for Dimitar Berbatov but left the door open for an "exceptional" opportunity.
"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 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."