My 2 cents:
If it is true that Wolfsburg has set a price of 57 million pounds, then at least KDB will have indicated to them that he will prefer to leave. He may not have handed in a formal transfer request, but at least given the indication. Otherwise it would be very easy for Wolfsburg to completely refuse to discuss any price.
So I think there is still leverage left in this saga.
Now, we have to remember that also KDB has a monetary interest in this transfer. If it does not happen, and he stays with Wolfsburg, he may be happy, but he will loose at least the wage increase we offer, and he will run the risk that a transfer of this magnitude will never be possible for him again in the future. His agent will also loose. Why he would not hand in an official transfer request (if indeed this is the case) we don't know, but for sure he will also be sweating as the transfer windows approaches the end.
Wolfsburg will also have reasons to want this transfer, sooner rather than later. They may want to replace KDB, so if the transfer happens is should be as soon as possible for them. They also do not want an unhappy player if the transfer fails, and finally also they must be asking themselves, if they can achieve the same price in the future (remember they have said they do not expect KDB to see out his contract).
For City, I think the worst that can happen is that we simply pay the 57 million. By playing the waiting game however there is the possibility that KDB looses his nerves and forces the move (which would also probably reduce the price), or Wolfsburg loose their nerves and reduce the price.
A general question is off course whether City is willing to pay 57 million. I suspect this is well above the valuation, and that City therefore really is not prepared to do it. If we pay, it will cost in all future transfers, as everyone will up the price extra when City comes along. So it is just not the few millions more for KDB that are at stake here.
P.S. the same arguments can be applied to the Pogba saga, and therefore I am thinking that this may not completely dead either.