Dortmund want £5million for the 23-year-old but United are still to finalise a decision.
Dortmund director of sport Michael Zorc said: "I spoke to Shinji and his advisor last week and to date he is not willing to extend his contract.
"We have a Plan A and B and we will follow one of them. We won’t gamble, but he has a specific career plan and he plans to play in England.
"We have to accept that, even if we don’t find it good."