Rooney has been heavily linked with a big-money move to the Chinese Super League in recent weeks after falling out of favour under Manchester United boss Jose Mourinho.
But Redknapp believes the 31-year-old could still do a job at Premier League rivals Arsenal.
The former Tottenham boss says Rooney is the perfect player for Wenger, claiming the Arsenal manager is crying out for a leader.
Harry Redknapp says Arsene Wenger needs a leader like Wayne Rooney
Wayne Rooney has been linked with Manchester United exit
Redknapp told the Evening Standard: "Arsenal looked at him a few years ago so we know Arsene is a fan.
"He would improve that team overnight because they have an issue with attitude and he is a winner.
"I watched Arsenal the other night at Sutton and I know it was a difficult pitch but some of their younger players were getting caught in possession, losing it cheaply and were putting their team in danger.
"There was nobody there shouting: “Oi, f***ing liven up!” They get away with it all the time.
Arsenal FC Super Quiz: Part 2
Superstar strikers who could replace Wayne Rooney at Man United
Tue, February 21, 2017
If Wayne Rooney left Manchester United, who could replace him?
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Who could replace Wayne Rooney if he left Manchester United
"Nobody sticks the boot into them, whether that’s from the dugout or other players on the pitch.
"Rooney would be someone out there on his team-mates’ case, digging them out if they aren’t at it. That would be invaluable for Arsenal.
"Say what you like about Wayne but his experience and will-to-win is up there with the very best. I saw a couple of Arsenal lads lose the ball and just stand there against Sutton.
"You need Wayne out there on the pitch getting straight into their faces reminding them what’s what."