Having been deemed surplus to requirements at the Etihad Stadium, the England international is currently taking in a season-long loan at Serie A outfit Torino.
The Italian side have expressed an interest in extending his stay, but interest in the 29-year-old is building back home.
Liverpool have seen Simon Mignolet and Loris Karius fail to convince at Anfield, and Jurgen Klopp is prepared to explore other options at the end of the 2016-17 campaign.