The 20-year-old - who has already made 133 appearances for Schalke in all competitions in his short career - has been the subject of repeated Arsenal interest throughout the January transfer window.
And with Friday's transfer deadline in sight, Arsenal reportedly sent chief transfer negotiator Dick Law to Germany in an attempt to thrash out a deal.
Draxler's contract was reported to have a £37 million buy-out clause, a claim rejected by Schalke sporting director Horst Heldt on Thursday, who said it is highly unlikely that the Germany international will leave the Veltins Arena.
"We are happy to have such a world-class player in our lines. I am very convinced that Draxler will be playing for us in the Rueckrunde (second half of the season) but most probably beyond that," Heldt stated.
"We are not interested in letting Julian leave, and he has also not approached us about a transfer."
When quizzed about Law's visit to Germany, Heldt added: "I checked my office if someone was waiting for me, but nobody was there."
He also acknowledged that big-money offers for Draxler would be considered, before refuting the incorrect reports about a clause in his contract.
"Of course, there are always other clubs interested in him, and should someone make a serious offer for him, then we as a club have to professionally consider that," he continued.
"That does not only apply to Julian Draxler, but to every other player.
"That agreement (£37 million clause) was only in place for last year, from now on the transfer fee is up for negotiation."
Draxler has won 10 caps for Germany, scoring one goal.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.