Despite bidding to sign the Norway international from Red Bull Salzburg in January, Haaland eventually made the decision to move to the Westfalenstadion.
Although Haaland has a release clause in his contract which can be activated in the summer of 2021, Real Madrid are allegedly keen to secure the frontman's signature during the next transfer window.
According to the Evening Standard, United are prepared to rival Los Blancos in the race for the 19-year-old services.
Dortmund are unlikely to consider a quick-fire sale unless either United or Real are prepared to pay well in excess of £66m, the fee which will most likely be paid next year.
Haaland has netted 12 goals from his first 11 outings for the German outfit. body check tags ::