One supposes the question is "Who else is there ?". And who would even desire the job ?
There had been talk of Graham Potter and Eddie Howe but they are ensconced at major club projects.
Frank Lampard ? - His managerial career has hardly been glittering and I suspect such an appointment might not receive universal approval.
Steven Gerrard ? - As per Frank Lampard.
I don't invisage the FA considering a foreign manager.

For what it's worth Pochettino is the current favourite with Tuchel second and Brendan Rodgers third.
Eddie Howe is up there but if Newcastle want to keep him they can pay him a fortune.

I suspect the appointment of a foreign manager would not be well received by the general public.

I believe Pochettino has expressed an interest in managing a national team.I do not know if Messrs Tuchel and Rodgers have any desire to manage on the International stage with limited access to players as opposed to the day-to-day involvement and games on a regular basis.

I have just been informed that current manager of Argentina, Lionel Scaloni, was signed on loan for W.Ham by Alan Pardew.

I found it all rather ironic that a player who was considered too old for the PL and considered by many (on these boards too in the transfer thread), as no longer capable of producing at the top level managed to sneak in front of a player who is considered by many to be no longer capable of producing at the top level, to head in the winner.