Has to be someone who is English, right? Cheating to have someone who isn't as a big football nation, again.
There aren't any established English managers with a glittering CV who the players in the England squad would respect. Potter could be good, if went to a a big club and was successful their first. If Southgate can get England to a WC semi final, with pretty much zero success at any other level of management, does it matter who we appoint? Also see Zidane, sometimes with very good players them actually listening to what you say is more important than experience.
So just anyone high profile from the prior "golden" generation, Beckham, Gerrard, Lampard, Terry, Rio, Campbell, or similar, they probably wouldn't be much if any better than Southgate, be entertaining at least though.