The Daily Mail says United are considering a swoop for Pulisic.
Pulisic, 19, is considered one of the brightest young talents in the world and is already a key man for Dortmund and the USA national team.
He made his first-team debut for Dortmund when he was just 16 years old.
United have maintained a 'watching brief' on the winger and the club have been putting together scouting reports.
Jose Mourinho reportedly wants to sign a new wide man and a playmaker in January.