The club have broken an impasse by agreeing a deal over wages and agents’ fee around any move that could materialise for their main target.
But there is still no guarantee of an agreement between the clubs before transfer deadline day on 5 October.
Sources close to Dortmund are adamant the club will not alter their demand for a fee in excess of £100m.
It had been suggested they needed to sell the 20-year-old, and would soften their approach as deadline day neared.
And United have indicated they would be willing to pursue alternative targets if Dortmund did reduce their demands.
Last week the Red Devils signed Netherlands midfielder Donny van de Beek from Ajax for £35m.
Meanwhile, sources have told BBC Sport that the impact of the coronavirus pandemic at Old Trafford will become apparent when the club releases their 2019-20 financial statement later this month.
It covers a period including the first three months of the coronavirus lockdown.
