The Old Trafford club are hopeful of landing the Borussia Dortmund winger, with the deal depending on whether both teams can agree a transfer fee.
According to Sky Sports, the Bundesliga giants want over £100 million for the 20-year-old star but United are unwilling to pay that much due to the economic impact of the coronavirus pandemic.
Dortmund are also determined for any transfer to be completed by the time they start their pre-season tour next month, so they have time to find a replacement.
It is understood that Sancho's personal terms will not be an issue in the deal and the Red Devils are the only club to have made contact with Dortmund regarding a deal.
The England international's contract expires in 2022 and the German side are relaxed about keeping him if they do not get their desired fee.
Ole Gunnar Solskjaer's chances of signing the player have been boosted by them securing Champions League qualification on the final day of the Premier League campaign.
United do have alternatives lined up if they fail to land Sancho, such as a loan deal for Bayern Munich winger Kingsley Coman, but are thought to have cooled their interest in Jack Grealish.
It is now unlikely that United will try and land the Aston Villa midfielder this summer.
However, Grealish is unsure about his future at his boyhood club, despite helping them avoid relegation from the Premier League.