Idk, from what I've seen City do their groundwork. We've heard very little about links from them to Rice besides the "X,Y,Z club that have money are monitoring the situation".
Maybe I'm being cynical, but I think West Ham showed City what was under their skirt to persuade them to bid on Rice. It's just so rare nowadays for a club to officially bid on someone and then immediately declare that they're out of the race.