Reus, who is currently sidelined with the ankle injury that kept him out of Germany’s successful World Cup campaign in Brazil, is contracted to Dortmund until 2017.
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However, this deal is also understood to include a release clause of around £27million, which can be activated from next summer.
As a result, Dortmund have tabled a new contract offer with an improved wage, but cancelling out the initial release clause, reports in the German media claim.
The country’s biggest national newspaper, Bild, understand that Reus has rejected the contract offer, giving the likes of Liverpool and Barcelona, two of the clubs supposedly chasing the 25-year-old forward, fresh impetus in their hopes to sign him.