Multiple ways, but starting with keeping Kane doing to the right things and not talking to the media the way he did both overtly and his camp did after (there would of course be the normal BS, but not to the level it got). Kane showing up at training, ect.
At that point I think Spurs and City got into a PR war and not a transfer one. A smart agent talking to both sides can smooth this type of transfer (even with behind the scenes indications that Harry won't play his best, doesn't want to get injured, ect.). But once the PR war was in full effect I think both sides went cold. They were some reports City probably was willing to go 130 but Levy wouldn't talk (and I'm not sure I blame him with the way Kane and City handled this). I think an agent could have helped all sides negotiate on this one from much earlier in the process.