Haller was picked up by Dortmund officials after landing at the city’s airport from where he was taken for his medical.
The 28-year-old Ivory Coast international is reportedly poised to ink a four-year deal with Dortmund to replace Haaland, who has joined Premier League champions Manchester City.
According to German daily, Bild, Haller’s transfer from Ajax is set to cost Bundesliga runners-up Dortmund around €31 million, including bonuses.
Haller was in superb form in the Champions League last season, scoring 11 goals in eight games, including four in a 5-1 win over Sporting Lisbon in Ajax’s opening group match.
The Dutch champions bowed out in the last 16, but Haller went on to score 21 goals in 31 games in the Eredivisie.
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