I know the old cliche 'just because you haven't heard of it before, it doesn't mean it did not happen' but not sure how much I believe that Man City interest because none of the reliable sources have even mentioned them before today.
As for Liverpool, again, I'm not sure how much I buy into this whole sub player or rotation player role for Werner. One of the main reasons why he decided to join us, after Liverpool pulled out, is that he's guaranteed more game time and will be an important player. If that is the case and Klopp had said he would be a sub player/rotation player at Liverpool in their conversation, why then Werner was still so intent on joining them? I mean for the longest time possible, we all know he wanted to join Liverpool but that didn't happen because they couldn't afford it and we managed to persuade him.
On a different note, maybe I have overestimated Liverpool's financial strength. Seems like they are paying a lot to their current players and are the Premier League's biggest spenders when it comes to agents' fees!
https://www.goal.com/en/news/why-liverpool-pulled-the-plug-on-54m-werner-as-chelsea/a1yjdfhc6i4e1rbor3o1xqytu