The 47-year-old is one of a handful of serious contenders for the job, which will become available once Wenger steps aside at the end of the season.
Neville is a big fan of the work achieved by Simeone at Atletico, where he has won a La Liga title, the Copa del Rey, Europa League and UEFA Super Cup, despite competing on a far smaller budget to that of domestic rivals Real Madrid and Barcelona.
Speaking on The Gary Neville Podcast, the Manchester United legend said: "Luis Enrique is the favourite, and I'm asking the question, looking at it from a football point of view, who is the right person to take over at Arsenal? Luis Enrique has been successful, but we discussed in the studio how good an opportunity is at Arsenal. What exactly is that opportunity? Is the opportunity to get Arsenal back into the Champions League? Or is the opportunity to get Arsenal to win the Premier League?
"If it is the latter, one of two things has to happen. They have to have a manager who can punch above his weight, and the second thing that can happen is Arsenal's board start to match the spending of Manchester City, Manchester United and Chelsea, but that isn't likely. So they have to have a manager who can punch above their weight, and the outstanding candidate for me is Diego Simeone at Atletico Madrid. Season after season he has challenged, not just in the Champions League but in La Liga too, with a team that has a big budget but nowhere near that of Barcelona and Real Madrid.
"What the new Arsenal manager is taking on with Man City and Man Utd, and to a lesser extent Chelsea, is huge financial might. £150m, £200m ploughed into the team each season. If you're going to compete with that, you have to have an outstanding manager to do so, and Simeone is that manager in Europe at this time. He has continually done it. To try and prise him away from Atletico Madrid would be the big move, and people say that wouldn't be the Arsenal way.
"But I dispute that strongly. The Arsenal way has changed over the years, and it wouldn't be ridiculous to suggest the new Arsenal way can be a little more pragmatic than the current team. Simeone is a winner, a fighter, he will culturally change everything. If Arsenal have aspirations to win the league, and are not going to do it by spending, they're going to have to do it by spending less and achieving more. That's difficult, and you need a special type of manager to do that."
Simeone's Atletico will face off against Arsenal in the semi-finals of the Europa League, starting with the first leg at the Emirates Stadium next Thursday. body check tags ::