United had offered £70million up front rising to £100m - but Dortmund wanted more up front and £108m overall.
While Sancho, 20, wanted the move, he did not want to force the deal by publicly announcing his desire to leave, says The Sun.
A public transfer request could have jeopardised his relationship with Dortmund if the deal did not go through.
He has told close pals that he is convinced he will still end up being a United player with a deal revived in the New Year.
The club have made it clear to the player that they will not turn their back on the move despite the problems they have encountered with Dortmund this summer.