Local newspaper Ruhr Nachrichten and Radio 91.2 claim the Norwegian and his high-profile agent Mino Raiola arrived at Dortmund Airport and were met by a BVB official the day after Salzburg's Champions League loss to Liverpool.
Haaland played 75 minutes against the holders but was unable to add to his impressive eight-goal haul in Europe this season.
Manchester United, Juventus and Real Madrid are among the other heavyweights reportedly showing interest in the 19-year-old.
Speaking after Dortmund secured their passage to the last 16 of the Champions League, Dortmund's sporting director Michale Zorc would not be drawn on the club's alleged interest in the talented teenager.
"We will not comment on this personnel question, but also on other personnel questions in the room, on the rumors that we constantly read, that we hear," Zorc said.
However, manager Lucien Favre called the potential move 'logical.'
"I think a club like Dortmund and others must always be interested in young players all over the world. That's quite logical."