Sancho spent last season on-loan with Chelsea, though the Blues passed on taking up his £25m permanent option.
Il Corriere dello Sport says United have now accepted an offer from Juve for £21.5m this week.
However, England international is yet to agree personal terms with the Bianconeri.
Along with Juve, former club Borussia Dortmund are also interested, though they are pushing for a loan-to-buy arrangement rather than the Bianconeri's outright offer.
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Sam81468
38
Borussia Dortmund thinks they’re the smartest in football business, they sold Sancho to United for £73m and took him back on loan to play for them and still wanted to sign him on loan trying to deceive United that they’ll sign him on a loan to buy terms knowing very well that his contract left only this season with United. First I thought United were smart when it comes to football business until I met Dortmund and Chelsea