Gunners representatives are due to travel to Germany to try and push a deal through for the £35million-rated midfielder.
The clubs are expected to hold talks, but the Bundesliga side remain reluctant to sell this month, even though Draxler himself is keen on the switch.
Arsenal see the 20-year-old as having the potential to develop into a striker in the future.
Wenger has a history of developing players into world-class forwards, having done so with both Thierry Henry and Robin van Persie in the past.
It remains unlikely Schalke will sell this month, but Arsenal are determined to make one more big effort to land a player they believe can have a major impact on their title challenge.
The Premier League leaders know they could face more competition for the player in the summer, and so are desperate to get a deal tied up as soon as possible.
Draxler is likely to be sidelined until March with an injury, but that has not put Arsenal off making one more bid.
Meanwhile, Arsene Wenger is expected to confirm the signing of a new contract within the next two weeks.