Draxler, who is said to have a £37million buy-out clause, has been touted as a potential target - with some reports suggesting the player had been spotted on a tour of Arsenal's Hertfordshire training complex.
Wenger, though, insisted nothing was imminent.
"That's like an unidentified flying object - some see them everywhere," the Arsenal manager said.
"I am curious as well (to see what will happen), but the transfer period lasts until the 31st of January.
"Are we close to signing anybody? At the moment I would say no."
Wenger added: "The transfer market in January is a low key transfer market.
"There is very reduced activity (generally). There will be some of course, but in the last three days as always."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball