The 19-year-old has drawn interest from a number of clubs across Europe since breaking into the Dortmund first team and has scored three goals in his 19 Bundesliga appearances so far this season.
Sport Bild reports that Pulisic is drawing particular interest from the Premier League, having previously expressed his desire to play in England one day.
Liverpool and Manchester United are expected to battle it out for the signature of the United States international, although they could also face competition from Bundesliga champions Bayern Munich.
Dortmund will command a hefty fee for the youngster wherever he goes, with Pulisic seen as a marketing tool in the United States as well as player with plenty of potential on the field.
Pulisic previously lived in England for a year, during which time he played for the youth team of non-league Brackley Town.