Dortmund already turned down an offer of £ 67m ($ 95m) earlier this month and while their latest offer is still below the asking price, all parties are confident that a deal will be struck.
The England international has already agreed on personal terms after a deal to bring the right-winger to Old Trafford last summer failed due to a dispute over the fee.
What do we know?
It now looks more and more likely that Sancho will be Man Utd's first signing this summer.
Ole Gunnar Solskjaer was a longtime admirer of the former Manchester City man and tried to sign him last summer, only United failed to reach the price set by the Bundesliga club.
The fee is believed to be around £ 77 million (€ 90 million / $ 107 million) this year, meaning United's current bid is below the offer price. Despite the discrepancy, this time it is hoped that a deal will come about, although it still has to be clarified how exactly and in how many instalments the fee will be paid.
Who else does United want to sign?
A centre-back is also on the shopping list, with Real Madrid defender Raphael Varane topping the list. He is believed to be looking for a challenge outside of the Bernabeu and United are keen to sign him, although an agreement on a fee would be required.
Villareal defender Pau Torres will also be of interest if a deal fails for Varane.
United are also considering signing Kieran Trippier even though the club and Atletico Madrid are far apart on their ratings of England. A central midfielder is also on the shopping list.
What about other offers?
Other transfer news assumes that United has not yet decided on Diogo Dalot before the new season.
The club is ready to sell him but Goal is aware that the price they paid to AC Milan, whom he was loaned to last season, is currently too high.
The Portugal international is open to another loan but would also be willing to fight for his place on Solskjaer's side if necessary.
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