Man City need Sterling. There aren't many available English players that fit their profile... in fact I'd probably say there are a handful.
If I'm not wrong, right now, they don't necessarily need English players to meet the current FA Home-grown player rules or the Champions League List A 4+4 (club-trained + association-trained) rules. I think the rules do not have restrictions on player nationality - they only require the player to have been registered for 3 years with the club or another club under the same FA before they were 21 (and I think there might be a lower bound too, like from 16 to 21 or something). A lot of these guys will be English of course, but not always.
They will need English players though, if Dyke's proposed change to the home grown rules gets approved.