The Daily Star reports that Mourinho wants to make an offer of around £25million for Draxler in the January transfer window.
Schalke general manager Horst Heldt has recently insisted that Draxler’s future is in the Bundesliga.
“Julian Draxler will be at our club this season, that is for sure,” Heldt told Kicker-Sportmagazin.
“There will be no fuss regarding him during the January window as he is committed to our club.”
The 20-year-old has also been linked with the likes of Arsenal, Manchester City and Manchester United.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.