In his two seasons with the German outfit, the Netherlands international has contributed 33 goals from just 66 appearances in Bundesliga.
Although the 27-year-old has a contract until 2023, the financial implications of the coronavirus pandemic will lead to clubs making more business decisions, rather than purely footballing ones, than usual.
According to Bild, this has resulted in Arsenal and Newcastle becoming contenders to sign Weghorst for a fee in the region of £32m.
From Arsenal's perspective, the deal may make sense, with any funds generated from the sale of Pierre-Emerick Aubameyang able to be used on bringing in Weghorst.
Meanwhile, should Newcastle be taken over by a Saudi Arabia-based consortium, Weghorst would be regarded as a major target after the poor return of Joelinton this season.