The 20-year-old Germany midfielder was a second-half substitute in the 1-0 win over England at Wembley on Tuesday night.
While Draxler openly admits he is a big fan of the Barclays Premier League and has been linked with moves to both Arsenal and Manchester United, he insists his full focus this season is on making continued progress with the Bundesliga side to secure a place in Germany's World Cup squad for Brazil.
"For my club, I have the chance to play nearly every game, it is important for me to improve myself," he said.
"I have said every summer I have to look what is the best for me and I will do in the summer again and we will see what happens.
"But no way. I won't switch then (in January)."
Germany's goal at Wembley was scored by captain Per Mertesacker with a towering header late in the first half.
The 6ft 6ins defender has settled well at Arsenal, where he was joined in the summer of 2012 by fellow German international Lukas Podolski, with club-record signing Mesut Ozil arriving for £42million on transfer deadline day this September.
Draxler has only heard "nice things" about life at the Emirates Stadium, with the Gunners currently top of the table.
He added: "I have always said English teams are very big clubs and Arsenal is of course one of them.
"Of course, I sometimes speak to Mesut or Per about the team, about the club, and they always have good words and they tell me nice things.
"You never know what happens in the summer, but Arsenal is a very, very nice team.
"They always have very young players, they play attractive football and that is what I like.
"But I better not speak too much about it because tomorrow I can read in the (English) newspapers that I like to play for Arsenal - I think the people at Schalke would not like to hear that."