The Czech Republic stopper left Chelsea and made a switch to the Emirates in 2015 and has one year left on his contract with his current employers. Joe Hart, on the other hand, was not included in Pep Guardioala's plans at City for this season.
Hart was allowed to join Torino on a season-long loan deal late last summer and the England international is aware that his career at the Etihad is over. According to the Italian publication Tuttosport via talkSPORT, Liverpool are looking at the option of signing the 29-year-old. The Reds are likely to face competition from Torino, who are hoping to sign Hart on a permanent transfer.
Parlour believes a move to Anfield will be a "good fit" for Hart as he thinks other top clubs in the Premier League are unlikely to make an approach for City goalkeeper.
"I'm sure that if Joe Hart wants to come back to England they'd be quite a few takers in the Premier League," Parlour told talkSPORT.
"I can see him definitely coming back to England, but maybe not right at the top level - not to Chelsea, Manchester United or Tottenham. Liverpool would be a good fit for him, but other than that you're looking at a mid-table side."
"I think Arsenal should stick with Petr Cech. Cech has been there and done it in big competitions – he's won the Champions League and Premier League titles."
Jurgen Klopp has the services of Simon Mignolet and Loris Karius as the two first choice goalkeepers at Liverpool. The latter arrived at Anfield from German outfit Mainz and the duo have struggled to impress at the Merseyside club.