Wenger claimed when speaking to the club's in-house media on Thursday morning there were no imminent deals, with reports chief transfer negotiator Dick Law had travelled to Germany to push through a big-money deal for the promising German international.
The Arsenal manager has long been an admirer of 20-year-old attacking midfielder Draxler, said to have a £37million buyout clause and who would go a long way to compensate for the loss of England forward Theo Walcott to a season-ending knee injury.
Draxler is currently recovering from an ankle tendon problem and so would not be immediately available to boost Arsenal's bid to get back ahead of Manchester City in the Barclays Premier League title race, or indeed for the upcoming Champions League tie against Bayern Munich.
Schalke sporting director Horst Heldt told a news conference he was "very convinced" Draxler would remain at the Gelsenkirchen club for the second half of the season and "most probably beyond that", insisting the Bundesliga side were "not interested in letting Julian leave" and also that the player had "not approached us about a transfer".
Wenger remains keen to bring in some offensive cover, although Mirko Vucinic's agent insists the Montenegro international is set to stay at Juventus amid reports of a loan switch to the Emirates Stadium.
"Are we active? Yes. Are we close to signing 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."
Despite being overtaken by free-scoring City on Wednesday night after they were held to a 2-2 draw at Southampton 24 hours earlier, Arsenal could return to the top of the table if they beat Crystal Palace on Sunday afternoon, with their rivals not in action until Monday night when they host Chelsea.
"We have to look at ourselves and only think we have to move forward," Wenger said.
"If you continue to move forward week after week you will make the difference.
"The kind of performance we delivered at Southampton will not move us forward, so let's focus to come back on Sunday and produce a good performance.
"Our future lies there, to be capable to repeat a top-level performance that demands top-level commitment in every single game.
"This team has commitment, character, intelligence and when we were questioned we always respond well. That's what is at stake on Sunday for us."
Midfielder Mathieu Flamini, meanwhile, will start a three-match suspension following his red card at St Mary's, but Czech playmaker Tomas Rosicky could be available again following surgery on his broken nose.
Jack Wilshere should recover from his ankle problem in time to face Liverpool next weekend, although Wales international Aaron Ramsey's setback with his thigh injury means a longer recovery for him.