The German international has been heavily linked with the Red Devils for some time, with the club set to go about a massive summer of transfer activity.
Reus has been one of Dortmund’s star performers in recent seasons, yet talk has been circulating suggesting that he could leave the club.
It is thought that the sales of big name players such as Mario Gotze and Shinji Kagawa have annoyed some senior stars, and with Robert Lewandowski set to also move on in the coming months unrest is liable to grow.
United are keen to take advantage of this, with incoming manager Louis van Gaal due to be handed around £150m-£200m to spend.
Reus is likely to cost around £25m, and is seen as a top quality addition.
The player himself may be keen on United, with the Red Devils certain to make him a key man at the club and offer him a lucrative deal to leave his homeland.