The 19-year-old has been linked with several major European clubs, including Manchester United and Liverpool, after scoring eight goals in six Champions League group games for the Austrian side.
He has been heavily linked with a departure from Salzburg during the January transfer window.
And Sky in Germany reports that he visited Bundesliga club Leipzig on Wednesday morning before flying to Dortmund.
A move to Leipzig is considered by some to be the most likely outcome, as they are affiliated with Salzburg as a part of the Red Bull group.
But Dortmund are keen to bring in a new striker after losing Paco Alcacer to injury, while United, Liverpool and Juventus have also shown interest.
Leipzig are hopeful that they can convince the 19-year-old that his development would be best served by playing under coach Julian Nagelsmann for the youngest squad in the German top flight, before moving on to an elite club.
Scouts from 40 different clubs across Europe were at the Red Bull Arena on Tuesday, largely to watch Haaland in action against Liverpool, as interest mounts.
In total, the Norway international has 28 goals in 22 appearances this season.
QUIZ! Can you name the top four at this stage of every Premier League season?
BACK TO SQUARE ONE Ajax are stuck climbing a ladder they can never reach the top of