There’s talk that England should be managed by an "elite" English manager. Howard Wilkinson is the only English league winning manager that is still alive but I doubt they would go for him at 81 years old.
As for English fa cup winning managers, there is only Keith Burkinshaw,81, Harry Redknapp,77, and Ron Atkinson,85, and Joe Royle,75, who are still alive.
There are basically no elite English managers out there that have ever won anything to choose from.