Sky Sports says United have seen a £91.3million bid for Sancho rejected by Borussia Dortmund.
The Red Devils have stepped up their chase to land their No1 transfer target with a first official offer made to the Bundesliga club.
But Dortmund are standing firm in their £108m valuation of the 20-year-old superstar.
The club have been adamant throughout the transfer saga they will not let him leave for anything below their asking price.
It would make him the most expensive Premier League signing ever, eclipsing the £89m United paid for Paul Pogba in 2016.
It was reported on Monday how United were preparing a £90m bid with just £65m of it paid upfront.
And now the Red Devils' latest offer has been turned down.