The Gunners made the Germany international their top target in the winter transfer window, and put 'big money' on the table in an effort to lure him to Emirates Stadium.
Schalke refused to buckle under pressure, though, and were able to retain the services of one of European football's hottest properties.
They may find themselves having to field further advances at the end of the season, with Draxler's contract including a buy-out clause, but general manager Horst Heldt is optimistic regarding their chances of keeping the talented 20-year-old - who is under contract until 2018 - in his homeland.
Heldt told Sport1 media: "Arsenal officially enquired about the services of Julian Draxler during the recent transfer window. We did not want him to leave.
"Of course, it was big money on offer, but still it was not enough for us.
"I am convinced Julian will be playing at Schalke past the end of the season. We are able to offer him enough ambition."