Greenwood, 18, received the No.11 shirt previously worn by United legends Ryan Giggs, George Best and Sir Bobby Charlton. The number was vacant after Anthony Martial took the No.9 shirt after Romelu Lukaku left for Inter Milan.
Williams will receive the No. 33 jersey previously held by Paddy McNair.
The No.11 shirt was one of the potential options for Sancho if he transfers to United from Borussia Dortmund this summer.
Sancho remains a priority transfer target for United who are still hoping to finalize a deal for the 20-year-old before the window closes on October 5. MEN Sport understands that United still have not come to a resolution on Sancho’s salary expectations and agent fees during talks with their representative Emeka Obasi and intermediary Marco Lichtsteiner, acting on behalf of Dortmund.
United fans believe the only logical option for Sancho is the No.7 shirt after Greenwood moved up to No.11.
United great Rio Ferdinand believes Sancho should only take the number previously worn by Cristiano Ronaldo if he can engage his long-term future for the club.
He said in May: “Yes I would [give him no.7], he’s that type of character.
“He’s got an arrogance about him, that’s what you want on a soccer field, they would take it. So yes, I would give it to him and I would put that pressure on his shoulders! “