I guess, but this sort of just happened out of the blue. A new CB is definitely something has been needed for a while for City, so they could have ironed out all the crinkles a month or two back.
Piecing together things from the summer, it sounds like he wanted/expected to come to United, but when it became clear that we weren't going to bid for him (or not enough) then his people had to find someone else, as Otamendi has pretty much burned his bridges with Valencia. Otamendi is 27, and coming off far and away his best season ever and a good Copa America. It's really his only chance to command a good price, so it makes sense that his agent (Mendes, or someone at Mendes' agency, correct?) would push for a move.
United were known (or at least though) to have a CB as their #1 transfer priority. So tons and tons of stories are put out there linking United to him. So much so that pretty reliable word from inside United a few weeks ago said that we are not interested and would not be bidding on him, while also expressing annoyance at United's name being used to drum up interest in him.
Once Ramos met with Perez and it seemed likely that Ramos was staying, the Otamendi talk picked up steam again. But a couple of weeks passed with nothing, then in the last week or so, a lot of City talk started to emerge.
The timing of everything, including the Ramos situation, really makes it appear that they were waiting for that to play out to see if United would bid after Ramos fell through (or, if Ramos did move to United, if Madrid would bid).