The Germany international – who missed last year’s World Cup triumph through injury – is considered to be one of the Bundesliga’s finest attackers, despite BVB’s woeful start to the season.
Although a key man at the club, Dortmund are at risk of losing their star for as little as £20m in the summer, with a release clause in his contract due too kick in.
This has alerted a host of clubs – including Bayern Munich, Real Madrid, Chelsea, Manchester City and Liverpool – but United are eager to win the race.
Reports indicate that the 20-times Premier League champions have been talking to Dortmund recently to sound out the club ahead of a deal, which could happen over the summer.
As well as Reus, Mats Hummels is another player on United’s agenda, with the defender having been a target for Louis van Gaal since his Old Trafford arrival.