Hart has been linked with a move to Everton in The Sun, and initially it was written off as being a farfetched rumour.
However, after Hart’s poor Euro 2016 for England, there are some doubts over whether Pep Guardiola will want to keep him at City.
And Warnock said: “I think his confidence is shot. I think it’ll be the best investment Everton could make and I think it’s the right time, because Pep Guardiola will let him go.”
City are reportedly lining up a move for Marc Andre Ter Stegen, with Guardiola keen to replace Hart.
If Hart did move to Everton it would be an announcement of the Merseyside club’s intent, as they look to bolster their squad.
Everton are known to be on the look out for a new goalkeeper this summer, with Joel Robles the only senior stopper in their squad at the moment.
Hart would be a big name recruit, but question marks would linger of his confidence.
Hart had an awful Euro 2016, when he made two high profile errors, as England crashed out after losing to Iceland.