The German international, who has a reported release clause of £37 million, was heavily linked with a move to the club in January is also said to be attracting the attention of Bundesliga rivals Bayern Munich.
However the Bavarians recently ruled themselves out of a summer bid for the player - and now it seems Arsenal are the favourites to snap him up in the summer - if he decided to leave Gelsenkirchen.
On Friday Draxler was in action for Schalke against Hertha Berlin - and would have been pleased with coming out of the game with a 2-0 win courtesy of goals from Klaas Jan Huntelaar and Chinedu Obasi - but for Draxler the main talking point was a seemingly heated conversation with coach Jens Keller on the touch-line.
The two appeared to have a disagreement in opinion on the touchline with both remonstrating their points - leaving much guesswork in the press over what was said.
But now both have moved to clear up the situation:
Draxler said that the two had initially disagreed over the players running channels in the fixture - but after the debate the boss agreed with his star player:
"No big deal. We had a mixed opinion about a situation, then have discussed and both came to the conclusion that I was right. "
And before you think that sounds almost arrogant from the player Keller himself has confirmed he did eventually agree with his player:
"It was about running paths. I thought he would have to make way. He was of the opinion; another would have to let him go. In addition, we discussed and Julian was right. Empowered players are no problem for me. "
Player power in full force? Perhaps.
We doubt Arsene Wenger would be so forgiving on the touchline should one of his players question his methods.