The 20-year-old has been heavily linked with the Gunners, but his current boss feels he would be better off staying put for now
Goal revealed earlier this month that Arsene Wenger was weighing up a January move for Draxler, who has a contract with Schalke until the summer of 2018 and a release clause reportedly in the region of £40 million.
However, Keller feels Draxler should not rush into a transfer to a foreign league and pointed out that the youngster already earns good money at his current club, so financial gain should not be a factor.
"Julian is only 20 years old and has all the time in the world to go abroad," Keller was quoted as saying by Bild.
"In order to succeed in another league, you need a strong personality. Plus it's not like he's earning peanuts here at Schalke."
Draxler has developed into a key player at the Gelsenkirchen side since breaking into the first team in 2010-11.
He has made 24 appearances in all competitions for Schalke so far this term, scoring five goals in the process.