Henderson, who helped England to a fourth-placed finish at the World Cup, impressed his manager with his fitness levels and played 20 minutes in Tuesday's 3-1 pre-season win over Torino.
Alisson was not able to keep a clean sheet after being beaten by Andrea Belotti's close-range header, but his departure late on saw Loris Karius warmly welcomed back to Anfield by fans after his two costly errors in the Champions League final defeat to Real Madrid.
Liverpool, however, beat City three times last season - twice in the two-legged Champions League quarter-final, and their moves in the transfer market should make them serious contenders.
Liverpool signed Brazilian goalkeeper, Allison, from Roma this summer and he is expected to take Karius' position as Liverpool starting goalkeeper.
Jurgen Klopp says he has "no idea" what will happen regarding potential Liverpool incomings or outgoings in the final few days of the transfer window.
The former Reds defender told Sky Sports: "Everyone's talking about Liverpool and with good reason".
"I was not surprised, to be honest, but as a human being I was hoping for it and I loved it", he added. The only problem I had for the club was that I wanted to get some money: 'Sign a new contract and then we'll sell you!' But that wasn't really realistic, ' Klopp is quoted in the Liverpool Echo. Is it possible being different in a really hard world?
This lead to Karius being the subject of a wave of abuse on social media, some of it going way past the typical football jokes you would see after the games, with death threats amongst several vicious messages targeted at the German goalkeeper.