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According to The Sun, Arsenal are planning a move for Pulisic amid fears they could lose either Alexis Sanchez or Mesut Ozil.
Both players will be out of contract with the Gunners at the end of next season.
However, according to Bild ,Dortmund have no intention of selling the 18-year-old.
They say Arsene Wenger has an “extremely difficult mission” on his hands if he is to lure him to the Emirates.
The news will come as a blow to Liverpool, who are also reportedly keen on Pulisic.
Jurgen Klopp is said to be willing to part with up to around £26m to reunite with the 11-cap USA international.
Pulisic was learning his trade in Dortmund’s youth teams towards the end of Klopp’s time in charge of the German club.
However he has since broken into their first-team under Thomas Tuchel, making 12 top-flight appearances this season and scoring two goals in the process.
His current deal at the Westfalenstadion expires in the summer of 2019.