The report claims the competition to sign the highly-rated 20-year-old playmaker is fierce, with the four Premier League giants jockeying for position ahead of a potential summer bid.
But Chelsea can offer something Arsenal, Liverpool and City cannot - the prospect of sending Kevin de Bruyne to Schalke as part of the deal.
The Bundesliga club have been linked with a move for the out-of-favour Chelsea star, who impressed on loan with Werder Bremen last season.
Any offer that included De Bruyne would shave off a chunk of the reported £40m asking price for Draxler, but Schalke would still expect a significant fee as well.
Chelsea, Arsenal and Liverpool fans getting excited ahead of January should be warned though, any potential deal is much more likely at the end of the season.
As Draxler revelled in an interview with Bild, his release clause is only valid during the summer transfer window.
"The club is determined not to let me leave, and the termination clause added to my contract is valid only during the summer transfer window," said Draxler.