Allardyce's position is under threat after The Telegraph filmed him offering advice on how to bypass FA regulations on player transfers.
The England manager, who only took over from former boss Roy Hodgson in the summer, also negotiated a £400,000 deal to provide services to a fake firm in the Far East.
Express Sport understands the 61-year-old has been summoned to Wembley to discuss the allegations with FA bosses.
WHO IS SAM ALLARDYCE? EVERYTHING YOU NEED TO KNOW ABOUT THE ENGLAND MANAGER
And replacement names are already beginning to arise, with Bournemouth's Howe installed at 13/2 favourite with Betway to succeed the former Sunderland boss.
Howe secured Premier League promotion for the Cherries two seasons ago and the club remained in the top flight last term.
Bournemouth sit 15th in the league after winning two of their opening six fixtures.
Howe, 38, has also been linked with the Arsenal post with Gunners manager Arsene Wenger's contract expiring at the end of the season.
Crystal Palace boss Alan Pardew is also in contention for the Three Lions job at 8/1.
Pardew joined the Eagles last year after being let go by Newcastle and kept Palace up last term.
Former Hull manager Steve Bruce, who quit the Tigers this summer, was interviewed for the England post after Hodgson resigned following the defeat to Iceland at Euro 2016 and is a 9/1 bet.
Gareth Southgate is 10/1 but declined to be considered for the post in the summer, while former England manager Glen Hoddle is 14/1 to return to the post.
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Next Permanent England Manager:
Eddie Howe 13/2
Alan Pardew 8/1
Steve Bruce 9/1
Gareth Southgate 10/1
Glen Hoddle 14/1
Jurgen Klinsmann 16/1
Gary Neville 20/1
Guus Hiddink 25/1
Alan Shearer 25/1
Roberto Mancini 25/1
Claudio Ranieri 25/1
Arsene Wenger 25/1
Laurent Blanc 28/1
Louis van Gaal 33/1
David Moyes 33/1
Manuel Pelligrini 33/1
Harry Redknapp 33/1
Vicente Del Bosque 40/1
Mark Warburton 40/1
Jose Mourinho 40/1
Brendan Rodgers 40/1
Luis Felipe Scolari 40/1
Ryan Giggs 50/1
Alex Ferguson 50/1
Philip Neville 66/1
Odds courtesy of Betway