Southgate got relegated with Middlesbrough during his only spell managing in the premier league and considering Euro 2024 might be his final tournament with Eddie Howe taking over. Would a top 6, mid table or team fighting relegation consider him for the manager? For top teams I could see Spurs, Liverpool or maybe Chelsea giving him a chance one day not immediately after the Euros of course. Villa, Newcastle, Brighton are probably good shouts
I don’t think any top team will hire him until he actually proves it at club level. Even most midtable clubs would be hesitant. I think a club like Fulham or Palace could be interested if they’re going through a transition in coaching already.