Ronny Deila is in charge of Celtic at the moment, but the Norwegian will leave the Scottish Premiership giants at the end of the season.
Former Celtic goalkeeper Bonner believes that Moyes would be the perfect candidate to succeed Deila.
The former Republic of Ireland international has also suggested Brighton & Hove Albion manager Chris Hughton and Ipswich Town boss Mick McCarthy as possible candidates.
“I would love to see Davie Moyes come in and, of course, Brendan Rodgers has been mentioned, too,” Bonner told The Scottish Sun. “But Davie was at Celtic when I was there, he’s got fantastic experience and he’s still a young man.
“If he could get the team playing the way Everton did when he was boss I think the fans would enjoy that type of football.”
“Chris Hughton and Mick McCarthy should be on the list,” added the Celtic legend about the two Championship managers. “They’re both managers who have done exceptionally well.”
Moyes started his professional playing career at Celtic and knows the club well. Moreover, the Scotsman is a very good manager.
True, things did not work out at Manchester United and Real Sociedad for the 53-year-old, but what he achieved at Everton was remarkable.
With Rangers playing in the Scottish Premiership next season, the Bhoys need someone who can be trusted not only to win the league title, but also to guide the team to the group stage of the Champions League.