Manchester United manager Louis van Gaal has confirmed midfielder Darren Fletcher is having talks at West Ham United.
Blackburn Rovers have signed midfielder Jay Spearing from Bolton on loan until the end of the season
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 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 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."
Despite being outplayed by a much-changed Germany side, missing several of their own key men, attack-minded midfielder Draxler believes England can make an impact in Brazil.
"The World Cup always has its own rules and England also have a very strong team, so you never know what can happen," he said.
"I think you can be happy about the English team, it is very strong and a young team with players like Jack Wilshere.
"I like them a lot and I think you will play a good role in the World Cup."