If City paid around 110 million and added Sterling on top, we would pretty much arrive at around 160 million. I'd be surprised if Tottenham declined to get Sterling on top of 110 million in exchange for Kane.
According to
Transfermarkt, Sterling is worth 90 million right now so giving Sterling away is definitely not an option for Manchester City. In the worst case scenario, City might not sign any striker atleast until the winter transfer window. Pep will probably put both Mahrez and Sterling up front with De Bruyne backing them then see how it goes with this.
Gabriel Jesus and Torres Ferran are also a good option as the front striker for now though
Now Sterling plays on left wing and they already had Son on the left, so I don't think they actually needed with him when they already had a pacy player like that.
I honestly dont think that would work with Sterling however even if they need a player that would set up the pace then there is still Bale. Bale was pretty good last season with Tottenham though