The 19-year-old midfielder is widely regarded as one of the brightest young talents in the Bundesliga at the moment, and has attracted admiring glances from a number of top European clubs, including Real Madrid.
Gunners boss Arsene Wenger has been credited with an interest in bringing the Germany international to the Emirates Stadium, as he prepares to splash more than £70million on strengthening his Arsenal squad ahead of the 2013/14 campaign.
Draxler has impressed for Schalke this season, with a number of scintillating performances coming in the Champions League.
His fine form has also caught the eye of Old Trafford chief Sir Alex Ferguson, who is preparing a Manchester United bid to rival that of Arsenal and Real Madrid, according to talkSPORT.
The talented teenager has made no secret of his desire to one day move to Spain, having recently told Marca that it would be a dream to play at the Santiago Bernabeu.
That could put Real Madrid in the driving seat to secure Draxler's signature, however that won't stop both Premier League suitors from stepping up their interest when the transfer window reopens on July 1.