Haaland will have a £63m release clause in his Borussia Dortmund contract next summer and is expected to be the subject of interest from the likes of Man United, Manchester City, Chelsea, Bayern Munich, Barcelona and Real Madrid.
A recent report claimed that Rangnick, who has agreed a deal to become Man United's interim manager for the rest of the season before stepping into a consultancy role, is determined to sign Haaland.
According to Bild, Man United have promised to pay the German a €10m (£8.5m) bonus if he manages to bring Haaland to Old Trafford during next summer's transfer window.
The report claims that Rangnick's appointment was part of a 'clear plan' to sign the Norwegian, who has scored 71 goals and registered 19 assists in 70 appearances for BVB in all competitions.
The new Man United interim manager played a key role in Red Bull Salzburg acquiring Haaland from Molde in 2019 and is believed to have a close relationship with the 21-year-old's family.