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 keen on signing the £26m winger and to reunite with the 11-cap USA international.
Liverpool’s American owners are desperate to sign a marquee player from the States to promote football back home. At present, Pulisic is the most talented player from USA and is a priority target for The Reds.
Despite Arsenal’s interest, Bild are confirmed that if Pulisic is to join Premier League, it will be with Liverpool and no other club.