The left-back would like to see his old Arsenal boss take charge of the Three Lions.
The veteran Frenchman has been linked with the role in recent weeks after Hodgson resigned following the Three Lions' dismal Euro 2016 showing.
Sunderland boss Sam Allardyce is favourite for the job and could get it by Friday, according to The Times, but Wenger has talked up the position recently.
And Cole, who played under the 66-year-old for seven years, says that his former manager is well equipped to take England to the next level.
"If you asked me to choose a manager it would be Arsene Wenger. I think he could develop it on to the next level," he told Sky Sports' Soccer Am show.
"Like I said, the players they have there is great talent. They just need the experience and just need someone like Wenger that can nurture the young ones, he's done it at Arsenal for years now so I'd like to see Arsene Wenger."
A lot of Arsenal fans would not mind seeing Wenger take the England job if it meant he left the North London club.
Wenger could celebrate 20 years in charge of the Gunners in September, but the last 12 of those have been disappointing as the former Monaco coach tries and fails to deliver a first Premier League title since 2004.
Frustrations looked to have reached boiling point toward the end of last season as Arsenal finished runners-up behind Leicester City.
It might've been Arsenal's last chance to win the title under Wenger again as the competition soars this season, with Jose Mourinho, Pep Guardiola and Antonio Conte helping to alter the landscape of the division.