The Frenchman is thought to be in the market for an attack-minded player following a season-ending injury to England international Theo Walcott, who ruptured his anterior cruciate ligament earlier in January.
Germany international Draxler has been touted as a possible replacement, with reports on Friday suggesting a deal was close to being agreed.
However, Wenger denied those reports, saying: "There is nothing happening. That (the Draxler rumour) is an illusion.
He added on BT Sport: "There is no news about that at all. At the moment some other clubs make the headlines, we don't."
Wenger was speaking after his Arsenal side reached the fifth round of the FA Cup with a comfortable 4-0 triumph over League One outfit Coventry City at the Emirates Stadium.
Forward Lukas Podolski did much of the damage with a first-half brace, the German first rounding goalkeeper Joe Murphy to fire into an empty goal before applying a back-post header following a neat set-piece.
Coventry improved after the break and hit the post through wantaway striker Leon Clarke, but substitutes Olivier Giroud and Santi Cazorla added further goals for Arsenal in the closing stages.
"In the first half we did the job and took the game to them in a serious way and played the way we know we can," added Wenger.
"In the second half we dropped off and, give them credit, they gave it a go. Coventry should be pleased with their performance and we should be pleased with the result."
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