The Frenchman ended a 22-year spell as Arsenal manager in the summer of 2018, following repeated calls for him to leave from a vociferous section of the club’s support.
But his successor Unai Emery could only lead the club to fifth place last season, before being sacked at the end of November following a disappointing start to the 2019/20 campaign.
Cole suggested that the fans who had called for Wenger’s head might think differently now, while backing his former team-mate and current interim boss Freddie Ljungberg to get the job permanently.
"There were a lot of people saying 'Wenger out’,” Cole told Sky Sports.
“Then Wenger went and maybe they understood what he actually did for the club and how he kept it together.
"Arsenal are in a transition period - they tried Emery and for whatever reason it didn't work out.
"Freddie is there and hopefully he can take over as permanent manager - he knows the club inside out.
"Freddie was my friend at Arsenal and hopefully he can change some things there."
Former Chelsea manager Carlo Ancelotti has been heavily linked with the managerial post at the Emirates after being sacked by Napoli earlier this week.
And Cole only had good things to say about the Italian, who he worked under at Stamford Bridge.
"Carlo did magnificently with the team,” he said.
“I liked how he was, not just as a manager but as a man. He was like your best friend."
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