Chelsea and Arsenal have been heavily linked with the young Germany international, with the Gunners in particular thought to be extremely keen.
Speculation over the January transfer window suggested Arsenal had submitted an offer for Draxler, although Schalke turned down as it "was not good enough."
They are thought to be holding out for the full value of his release clause, which totals €45m.
And Bayern Munich, who have a long history of snapping up the best Bundesliga talent, could beat Arsenal and Chelsea to his signature this summer.
Bayern signed Mario Gotze from Borussia Dortmund last year, with Dortmund striker Robert Lewandowski set to join him at the conclusion of the current campaign.
Schalke are obviously desperate to keep Draxler at the club, but they may find it difficult with the likes of Chelsea, Arsenal and Bayern circling.
Having said that, the fact that it's a World Cup year could play into their hands.
If Draxler impresses at the tournament in Brazil, Schalke would be in a much stronger position to demand his full €45m fee to grant Draxler the freedom to move.