Or, to be more precise when considering the discourse of recent days, the nationality of any replacement.
“Unacceptable” was the response of Southgate’s predecessor, Sam Allardyce, to the notion the FA might consider appointing a foreigner.
Of course, it would be preferable for the England football manager to be English. There’s nothing against the rules in going overseas but there would be some embarrassment in one of the richest football nations once more having to admit it cannot find a suitable candidate on home shores.
But essential? It is just as well English cricket does not think that way, or who knows how they would have fared over the past decade when the biggest successes have been forged under the leadership of a Zimbabwean, an Australian and now a New Zealander as head coach.
One of the biggest requirements for any boss of the England football team, ability aside, is be a clear understanding of the size of the role they are taking on. It has always been a bit more than your average managerial post.
That is something which has undoubtedly served Southgate well. A former international player, who had already worked for the FA and coached the under-21s, he has always appreciated the job is almost as much about being a skilled politician as it is coach.
Though managing England might no longer be the most lucrative post in the land, it remains by some distance the highest profile. He is the manager whose team selections are scrutinised by more people than any other and whose life is considered, rightly or wrongly, public propertyy in the same manner as Rishi Sunak’s.
It feels fair to say Sven Goran Erikson and Fabio Capello, the two hugely successful managers previously appointed by the FA, never understood that. The level of press scrutiny baffled them and impacted their work.
After six years at the helm, it may be that Southgate has finally been worn down. Finding someone who can carry the load so impressively to replace him will not be easy.