As I've said a few times I'm of the belief that this crosses the finish line very late, once Tottenham have sorted themselves out.
In that timeframe it's in Tottenham's interests that it comes across like there's a very realistic chance Kane stays, so that potential selling clubs/agents don't rip them off. On the same front, it's in City's interests to back that up so as to not undermine Tottenham's efforts and compromise everything.
If Tottenham sign players for good value then they'll charge City less, but if City leak something out and Tottenham overpay then City might be forced to overpay themselves. I suspect that if push comes to shove City WILL overpay if they have to and are trying very hard to avoid this scenario.
I believe the reaction from both clubs to the wedding story was very telling.
Once we start reading from Tottenham that Kane isn't for sale, and confirm that he's staying, then we can start to feel a bit nervous. But so far it's all been about City not being willing to pay the fee, which is likely all PR.