Liverpool boss Jurgen Klopp recently admitted he is still unsure who his No 1 goalkeeper is between Loris Karius and Simon Mignolet.
Mignolet has played three of Liverpool’s four Premier League outings and both Champions League qualifying matches against Hoffenheim.
While Karius started in the 4-0 league win over Arsenal last month and was recalled for last night’s Champions League Group E opener against Sevilla.
And Neville believes England international Hart would be a step up from both of Klopp’s current goalkeeping options.
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Liverpool should have signed Joe Hart, says Phil Neville
I’m surprised he didn’t go out and get Joe Hart
Phil Neville
Speaking on Radio 5Live, he said: “I’m surprised he didn’t go out and get Joe Hart. A real top-class, experienced goalkeeper.
“I think he’s (Hart) better than what they’ve got. I think he would have given them a bit of stature at the back.”
City manager Pep Guardiola made it clear to Hart when he arrived at the Etihad last year that he is not in his first-team plans.
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The 30-year-old was sent out on loan to Serie A outfit Torino last term and was offloaded to West Ham on a season-long loan in the summer.
Hart has gone on to make 348 appearances since joining City from Shrewsbury in 2006, winning the Premier League twice, the FA Cup and two League Cups.
But he has endured a difficult start to life at the London Stadium, shipping 10 goals in his first four games for West Ham.