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
Part of it depends on how the Euros goes. If England do well again, or even win it, he might be able to land quite a good job - probably not the very best clubs the next level down might be within reach.