The German club's sporting director Horst Heldt recently confirmed that they had rejected a bid for the midfielder during the January transfer window, but did not identify the club involved.
Arsenal were reported to be the team who made an offer for the 20-year-old, who has returned to training following injury, and the Gunners could come back with an improved bid in the summer.
Heldt also said that Draxler's buyout clause of €45.5million was in place only for last year, but Keller admits that it can still be activated at the end of the season.
"I am delighted that we have him on board for the second half of the season but, because of his clause, he can leave when a club puts the money on the table," he told Bild.
"That's why I can't plan with him, because it is just not in my or our hands.
"It's a god-awful situation when, as the coach, you don't know whether such an important player will move on, but Julian was injured at that time, so at least any unrest did not necessarily affect the other players.
"He's young, but has made over 100 competitive appearances for Schalke. Others don't achieve that in five, six years.
"That's why he is very experienced already, and has shown his superior qualities often enough, although his youth shows in his consistency.
"It's clear that all the talk about his €45.5m release clause and the interest from top European clubs leaves its mark on such a young lad.
"The hype around him last summer was huge. He must learn to cope with that, and also that failing to perform at less than 100% is not good enough for him."