The United Stand reports United are readying their fourth attempt to sign the England winger.
They will submit an offer to their German counterparts of £85m for the 21-year-old.
It is an amount Dortmund will reportedly accept, having lowered their demands due to a number of factors including the coronavirus pandemic.
The Red Devils are expected to lodge the bid on Tuesday.
Sancho continued his impressive form in Germany by scoring 16 goals and provided 20 assists this season across all competitions.
His acquisition would make a stern statement to United's rivals heading into next season.
With a right-winger recruited, Ole Gunnar Solskjaer would turn his attention to signing a centre-back and midfielder.