The Borussia Dortmund winger has been on United's radar for 18 months but a £100milion asking-price, allied to the German club's reluctance to sell, stopped the move happening in the previous two windows, says the Daily Star.
Yet, though injury has hampered Sancho's progress this term, Reds boss Ole Gunnar Solskjaer remains a big admirer.
And that means the England international tops the list of possible big-money arrivals at Old Trafford ahead of the 2021-22 campaign.
United would still love to land Sancho's Borussia team-mate - Norwegian hitman Erling Haaland.
However, securing an authentic winger in Sancho, 21, is the priority with the Reds increasingly optimistic Edinson Cavani will agree a new one-year deal.