The 19-year-old attacking midfielder has been labelled as one of the hottest prospects in German football in recent seasons and a move to Arsenal or Chelsea was rumoured during the transfer window.
However, he rejected those advances and insists that he is happy in the Bundesliga after Schalke strengthened ahead of the deadline.
The arrival of Kevin-Prince Boateng particularly impressed Draxler and he hopes that regular football in Gelsenkirchen will help him cement a FIFA World Cup place next year.
"You always need time to get used to a new team," he told FIFA. "I'm convinced I'm at the right club with Schalke.
"We haven't had a great start to the campaign and I was a bit disappointed after the first few games, but I think we took another important step forward after signing Kevin-Prince Boateng.
"We've got a strong team."
Draxler has started every game for Schalke this season and made a last-minute appearance as a substitute in Germany's 3-0 win over Austria on Friday.
Jens Keller's side sit 13th in the table with four points from as many matches.
