United are the favourites to sign the 21-year-old, having tracked him for the last two years.
The Red Devils were keen on signing Sancho last summer but refused to meet Dortmund’s £108m asking price.
However, Dortmund have since lowered their valuation of Sancho to around £80m and that’s attracted more interested parties.
One of those includes Chelsea, with Thomas Tuchel said to be a huge admirer of the England international.
According to the Sun, Chelsea are ready to test Dortmund’s resolve with an £80m bid for Sancho.
Sancho was born in London and grew up as a Chelsea fan, which could work in the Blues’ favour.
The midfielder is keen on a return to the UK having left Manchester City for Germany in 2017, when Dortmund struck a £10m deal for his services.
Edinson Cavani’s contract extension at Old Trafford means United can afford to shelve plans to sign a striker for another 12 months, meaning they can focus their attention on signing Sancho.
Sancho would face greater competition on the right flank at Stamford Bridge, with Christian Pulisic, Hakim Ziyech and Callum Hudson-Odoi all capable of playing there.
United, by contrast, only have Mason Greenwood as a genuine out-and-out right winger. The likes of Daniel James, Marcus Rashford, Anthony Martial and Paul Pogba have all played there but prefer to play from the left.