BILD says United will look to beat Liverpool to sign Pulisic this summer.
The United States international is in great demand, as much for his marketing potential as his ability on the pitch.
The Premier League duo will join Bayern Munich to sign the 19-year-old.
Pulisic can play centrally or out wide and has always stated his intention to move to England at some point in his career.
Bayern will look to persuade him that his future remains in Germany though, with Dortmund in line to gain a huge fee.