The Independent says United and Dortmund appeared to be at a stalemate regarding the valuation of the 20-year-old, though an initial fee has now been struck.
Dortmund are said to now be happy to take an initial £60m payment for the player, with a string of added on clauses which could eventually sky-rocket the deal.
The Bundesliga giants appeared resolute in demanding £100m for the youngster, but the new deal is said to better suit United while appeasing both parties.
Talks are still 'between intermediaries' and have not yet reached the official stage of formal negotiations.
Sancho cost Dortmund just £7m from Manchester City in 2017, after he decided to leave English football in search of regular first team opportunities.