The Gunners have been told by the Germans that 20-year old attacking midfielder is not available, even for £37million, but Wenger is holding onto hope that he may still be able to land him before Friday's transfer window closes.
The Frenchman was also hopeful of making at least one signing prior to the winter market slamming shut.
"Are we active? Yes. Are we close to sign anybody? No," Wenger told Arsenal Player.
"There is not long now, that is true.
"First, the situation was going like always in a transfer market - week by week.
"In the last two weeks it goes day by day, now it goes hour by hour.
"In any hour, anything can happen or change, but at the moment, unfortunately, we are not signing anybody."
Schalke sporting director Horst Heldt had said earlier on Thursday that Draxler was certain not to be leaving Gelsenkirchen this month.
"We are happy to have such a world-class player in our lines and I am very convinced that Draxler will be playing for us in the Rückrunde [second half of the season] but, most probably, beyond that," Heldt said.
"We are not interested in letting Julian leave and he has also not approached us about a transfer."
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