Toure is set to leave the Premier League champions after eight seasons at the Etihad and the former Manchester United defender has backed him for a move to the Emirates.
And Neville thinks recruiting the 35-year-old could help resolve some of that.
“We were talking about Arsenal, about having that strength in midfield, the character and the leadership,” he told Sky Sports.
“To be fair they could do worse than maybe have him for a season to sort out the culture in there.
“You’d have to play him in midfield; you couldn’t play him at the back.
“You’d have to play him in midfield and get people around him with legs.
“In his first three or four seasons in the Premier League , he was outstanding, he was one of the most dominant forces.
“You talk about (Vincent) Kompany, Yaya Toure, (David) Silva, (Sergio) Aguero; they are the Manchester City players who mostly transformed Manchester City from being nowhere near winning a title to being champions of England.”
Manchester City celebrated Toure’s contribution to the club’s success in recent years.
Toure very nearly joined his older brother Kolo in north London back in 2003.
The powerful midfielder had a trial with the Premier League club but a permanent move never materialised.
Speaking in 2014, Wenger revealed the club wanted to sign the Ivory Coast international, but the logistics proved too difficult.
“It would be up at the top [of my list of regrets],” he said. “But let’s not forget that Yaya Toure had an agreement with us – and it’s not because we did not want to sign him that he went to Ukraine.
“We needed to wait for his passport in Belgium. We have made mistakes but he is not a mistake, it’s just the fact that he preferred to go to Metalurh Donetsk. He could go there without any passport.”