Max Meyer has turned down Schalke's second contract offer, with German outlet Sport Bild linking him with both Arsenal and Barcelona.
Meyer's current deal expires this summer and he rejected the first offer of another last year.
The 22-year-old Germany international has since become a crucial part of coach Domenico Tedesco's lineup, having moved from attacking to holding midfield.
Schalke had hoped to persuade him to stay with a second offer that would have made him their top earner with a reported annual salary of €5.5 million.
However, sporting executive Christian Heidel confirmed the approach had been turned down.
"Max Meyer's agents, on Jan. 12, received an offer limited until Feb. 15, and on Feb. 15 informed us via email that Max has turned down the offer because of the time limit," Heidel told Der Westen.
"We duly noted it and for now are not bound by it. This does not mean that he will not prolong his contract."
Heidel upped the pressure on Meyer, saying that "Schalke must press forward with their planning for the new season."
And speaking to Sport Bild, he added: "If Max Meyer approaches us and says he wants to continue playing for Schalke, that's wonderful. But we can't and won't wait for much longer."