Sheffield United boss Chris Wilder is an early contender for the manager's job at Huddersfield Town.
David Wagner left the post by mutual consent on Monday night.
The Daily Mail says Under-23s coach Mark Hudson will take charge for Sunday's clash with Manchester City but is not expected to be offered the role full-time.
Chief executive Julian Winter is known to be a fan of Sheffield United manager Chris Wilder but no approach has yet been made.
Sam Allardyce, who played for Huddersfield, is not understood to be considering an application.
While they acknowledge that the situation is grave, officials at the club retain an element of belief that they can stay in the Premier League and will be looking for a candidate who shares that view.