The 19-year-old penned a new contract in May to keep him at the Gelsenkirchen club until 2018, after insisting he would remain at the Bundesliga outfit for the upcoming 2013-14 season.
However, following concrete interest from Borussia Dortmund, Draxler says a move to the two Premier League giants, plus Real Madrid and Barcelona, could see him leave the Veltins-Arena.
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The attacking midfielder, who has six caps for the national side, has a €45.5 million [£38m] release clause, and the player's representative, Roger Wittmann, insists the full figure will have to be met to trigger a departure from Schalke.
"The player costs 45.5 million, and he has to agree. These are the conditions of the transfer," Wittmann told Bild.
Reports in the British press on Wednesday have linked new Chelsea manager Jose Mourinho with a move for Draxler, but the Schalke sporting director, Horst Heldt, has insisted the Blues are yet to confirm any interest.
Heldt told Bild: "There has been no official transfer enquiry from Chelsea. and we are not in contact with them.
"But, it must be noted, there will always be interest in players with the qualities Julian Draxler has."