"The situation is now different. Manchester have made a much improved offer," Watzke told Sport Bild magazine.
"In situations like this there are always a lot of different things to consider and in the end at one point we have to make a decision.
"As we are back in training on Monday we will decide at the weekend. I have contacted the relevant people and we will weigh things up ...then the board will make the decision."
The 27-year-old scored 11 goals in 31 league games as Dortmund finished second last season and could be Mourinho's second signing at United after defender Eric Bailly's arrival from Villarreal.
(Reporting by Ian Rodricks in Bengaluru; Editing by Greg Stutchbury)
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