Wenger announced last week that he will be standing down as Arsenal manager at the end of the 2017-18 season following a difficult campaign.
Arsenal are in sixth spot in the Premier League table but could still secure a Champions League spot if the Gunners win the Europa League.
The north London side have been linked with Juventus manager Massimiliano Allegri, New York City FC head coach Patrick Vieira and former FC Barcelona boss Luis Enrique.
Wenger will be leaving the Gunners after 22 seasons since his appointment in 1996, yielding three Premier League titles and eight FA Cup crowns.
Manchester United are still recovering from Sir Alex Ferguson’s retirement in 2013 and his immediate successor Moyes lasted 11 months in the job before he was axed.
Former Manchester United captain Keane predicted that the next Arsenal boss will fare better than Moyes.
“There was a lot of pressure on David Moyes and he didn’t get a chance, particularly with the recruitment of players,” Keane told ITV Sport.
“I think it’s a touch easier (for the next Arsenal manager). There are problems at Arsenal but it is still a great job and a lot of managers would love to manage Arsenal and get them back competing for league titles.”
Arsenal haven’t won the Premier League title since 2003-04 when Keane was still captain of Manchester United.
The Red Devils will take on Arsenal in their next Premier League game at Old Trafford this weekend.
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