Klopp has come out and said Coutinho is mentally on-board, but is being left out of the squad to give him time to build fitness. It's plausible, given that he only played 20 mins or so in each of his outings for Brazil, but nobody really believes that his absence from the squad and from training was completely down to some mysterious back injury.
This is especially true given how Brazil's physio overcooked what should have been a routine lie by saying Coutinho's back injury was the result of stress, with clear implications as to where that stress was coming from...the negotiating table with Barca. He certainly looked fit enough when playing in a Brazil shirt...
Nevertheless, all will be forgiven if he comes back soon and plays well. Klopp has negotiated the situation with a clever (if still transparent) series of platitudes and white lies designed to make it clear to fans and the media that the player's head was turned and he'd better un-turn it quickly, after which every thing would be hunky-dory.
Liverpool could certainly use him, at least off the bench, for this weekend, but Klopp is either giving him a lesson or really does see a slight lack of fitness.
I think Liverpool have every chance of a win or draw at Man City, especially if they score early. Man City will probably control the midfield, but with Mané and Salah attacking the flanks I think there should be plenty of opportunities to get behind Pep's defense and cause big problems.
EDIT: Vincent Kompany picked up yet another injury while on international duty hammering Gibraltar 9-0, and will not play this weekend. Man City have spent a lot of money bulking up their back line, but they are always weaker without Kompany. Could be a factor against Liverpool.