Anyone who does not speak English should be avoided. As a long term strategy, say you are getting them ready to join in the summer, fine, they can learn the basics between now and then. But if joining straight away, mid season, it could potentially be a car crash, ala G Nev at Valencia. Naturally a lot of modern managers speak multiple languages, Guardiola, Tuchel, Klopp all seemed to have a basic (Or better than most here and in the UK) grasp of English already, but if we are looking at a translator for everything a manager does it would be concerning. 2 common links at the moment are Zidane and Ten Hag. I have read Zidane doesn't speak much English, so I would want to avoid that (Regardless, it is rumoured he doesn't want a PL job because of it), and Tottenham supposedly decided against Ten Hag due to his English not being great, so I would be wary about both.
The second thing I would want us to avoid would be a purely defensive/negative manager. It's difficult because they don't always start out that way, but a Simeone/Allardyce/Hodgson/Mou/Conte type manager should be avoided, especially with the current crop of players, too many of our better players can't/won't fit that style, and on top of that confidence is low with the players as is, if we have a manager come in like that, the already difficult home games could become unbearable.
I'm not really bothered about past links to teams though. Generally you expect managers to be professional, even players, like Carragher being an Everton fan, Solskjaer a boyhood Liverpool fan, it never impacted their playing careers, and managers are exactly the same. So I wouldn't care less if a qualified/decent enough ex Liverpool/City player or manager got appointed, because it would be largely irrelevant.
