Haaland will have a £63m release clause in his BVB contract next summer, and the Norway international is expected to be the subject of interest from a number of the biggest clubs in European football.
Man United are said to be firmly in the race for the 21-year-old, who has scored 71 goals and registered 19 assists in 70 appearances for Dortmund in all competitions.
Rangnick, who has been confirmed as the English club's interim manager for the remainder of the season, played a key role in Red Bull Salzburg acquiring Haaland from Molde in 2019, and the 63-year-old is believed to have a close relationship with the forward's family.
According to former Red Devils coach Meulensteen, Rangnick's arrival at Old Trafford could help the Premier League giants secure the Norwegian's signature.
''Football is about relationships. We all know that Haaland is a tremendous talent with an unbelievable goalscoring record. He's young, he's direct, he's quick, he's strong," Meulensteen told Stadium Astro.
"I think like a lot of fans I expected him to be at Man United already because of that relationship with Ole Gunnar Solskjaer. They know each other but for whatever reason it hasn't materialised.
"It is important that you have got good relationships. Maybe Rangnick can bring something to the table and bring someone like Haaland to Manchester United. I think that would be a big scoop."
Haaland - also linked with Bayern Munich, Barcelona, Real Madrid, Manchester City and Chelsea - has scored 14 times and registered four assists in 11 appearances for Dortmund this season. body check tags ::