Yeah, he could very well be persuaded by the challenge of pitting his wits against the hotbed of top managers in the Premier League. But, it's hard to envision any good landing spots for him with the early success of Conte at Chelsea, the time and resources dumped on Guardiola's success by City, Mourinho at United unless we abandon the plan, etc. - and Arsenal's way of football is very different from El Cholo's robust and industrious style so there could be a potential clash of ideologies and mindset (though some would argue that the particular way stems only from Wenger and a fiery character like Simeone is exactly the type of manager the doctor ordered if Arsène leaves by mutual agreement).
Wrt. Inter, Simeone has historical ties with the club as a former player (much like Atlético), so a move would make sense on some levels because they have a good core with the likes of Icardi, Mário, Gagliardini, Murillo, Brozović; Zhang Jindong could make substantial investments in the team, and they could collectively re-establish the club as a force on the level of Juventus - that in itself would be more satisfying on an emotional level than success with clubs where he'll be very much of an outsider to begin with, and wouldn't share a comparable level of camaraderie with the supportbase.
eg. from 2013:
http://www.fourfourtwo.com/news/it-would-be-honour-coach-inter-says-simeone#IFIIeX46MovGZ47D.99
You may be right about his ties to Italy but I would prefer it if he'd join Lazio instead, I loved him there. But the problem is that Inter has the financial muscles and Lazio has Lotito. But former players usually say that they would like to return.
Simeone about Lazio:
“Lazio was a fantastic part of my career,” Simeone recalled in an interview with Lazialità.
“It’s one of the places where I spent the most time, I had four wonderful years there. The people always loved me, and slowly I was able to make them appreciate me as a player.
“I scored important goals which people will never forget. In Rome I had teammates and coaches who changed the philosophy of Italian football.
“Before, only Milan and Juventus ever won [the Scudetto]. With our arrival we changed that narrative, and also allowed others, those who live close to us [Roma] to do the same.
“I have many friends in Rome, and I’m sure that one day I’ll Coach Lazio, because that’s life.
“It happened when I went to a club like Atletico Madrid, where I had been [as a player] and given my everything to do well, so it could also happen with Lazio.
“I’m convinced that you go back to those places where you have a past as a player. I behave the same way in football and in life.
“I will return to Lazio, it’s only a matter of time. Right now I’m very happy at Atletico Madrid, but life is long, and one day I’ll be there, dressed in black as always.”