The Israeli was sacked immediately after the east London club were relegated from the Barclays Premier League on Sunday in the wake of the 3-2 defeat to Wigan - a game they had led 2-0 at half-time.
Co-owners David Sullivan and David Gold decided to take decisive action fearing a hostile backlash at Upton Park this weekend when the Hammers host Sunderland in the final game of the season.
Queens Park Rangers boss Neil Warnock, Cardiff manager Dave Jones and Notts County chief Martin Allen are all in the running.
In the frame: QPR boss Warnock
In with a shout: Cardiff's Jones
Shortlist: Notts County chief Allen
NEXT WEST HAMMANAGER ODDSSteve McClaren - 8/15
Neil Warnock - 9/1
Chris Hughton - 9/1
Sam Allardyce - 12/1
Gus Poyet - 14/1
Martin O'Neill - 16/1
Paolo Di Canio - 16/1
Dave Jones - 33/1
Martin Allen - on request
Odds courtesy of Paddy Power
West Ham could also consider relaunching a bold move to appoint Martin O'Neill, who they attempted to replace Grant with back in January.
Former England manager Steve McClaren has been tipped to replace Grant at the helm as the bookmakers favourite.
But Sportsmail Online understandsMcClaren, who West Ham wanted as Harry Redknapp's successor in 2001 before he rejected them in favour of Middlesbrough, is not currently on the club's shortlist.
West Ham co-chairman David Gold took his share of the blame for their relegation, posting on social networking site Twitter: 'This is undoubtedly the worst moment in all the years I've been supporting West Ham and I wish I'd done things differently
'I honestly believed with the players we brought in in January, plus the imminent return of (Thomas) Hitzlsperger, we had done enough to pull clear of danger.
'I know that Scotty Parker shared that belief with me and we both had confidence that we would retain our Premiership status.'
Kevin Keen will assume the caretaker duties on Sunday but the former Hammers midfielder is not considered to be in with a chance of succeeding Grant.
Axed: Avram Grant was sacked after West Ham were the first side to be relegated to the Championship this season
HAVE YOUR SAY. Who do you think is to blame for West Ham's slump? West Ham will play Championship football next season after they suffered an agonising defeat at relegation rivals Wigan on Sunday. Manager Avram Grant has already been sacked by the board, while Scott Parker will lead the exodus. But who do you think is responsible? TELL US WHAT YOU THINK Keenis likely to be kept on by the club in his capacity of first-team coachnext season under the new regime but a host of Grant's backroom staff could be moved on.
Senior coach Paul Groves and goalkeeping coach David Coles were both brought in by Grant from Portsmouth 11 months ago but now face an anxious wait over their futures.
The disappointment in the dressing room at the club's dressing room was revealed by first-team debutant Jordan Spence.
The highly-rated 20-year-old made his first senior start for the Hammers at the DW Stadium but admitted his joy soon turned into disappointment.
'The over-riding emotion at the moment is just huge disappointment,' said the England Under 21 international, who has spent most of the season on-loan to Championship side Bristol City.
'I don't actually have words to articulate how disappointed I am.
'Itwas my full debut on Sunday, but throughout the season, when I've been at West Ham I've been part of the squad. I've been part of the squad from the first day of the season to the last and it's hard to take,' he said.
Hammer blow: West Ham's players can't hide their disappointment after failing to beat the drop
'Wehave been relegated and we can't underestimate the Championship is a difficult league, but I can say that I and whoever else is out there will do everything we can to bring us back to where we deserve to be.
'We're a big club in the Premier League so we're an even bigger club in the Championship.'
Spence is likely to stay on at Upton Park but a host of high-earning first-team stars are certain to depart this summer with the cost of relegation estimated at ?40million by the club's owners.
Decision time: Co-owners David Sullivan and David Gold must choose a successor to Avram Grant in the Upton Park hot seat
Footballer of the Year Scott Parker is wanted by Tottenham while captain Matthew Upson is out of contract and heading for the exit door.
Robert Green, Danny Gabbidon, Kieron Dyer and Carlton Cole are also set to leave with on-loan Robbie Keane and Wayne Bridge ready to return to their respective parent clubs, Spurs and Manchester City.
Whoever replaces Grant in the hot seat will have to be ready to lead to the club's promotion charge under a tight budget and with a team of new faces.
Meltdown! Grant sacked as West Ham relegated after throwing away two-goal lead at Wigan We did it! Millwall fans group admits sorting plane stunt mocking AvramGrant is sacked - How Sportsmail exclusively broke the newsWigan 3 West Ham 2: N'Zogbia double condemns Hammers as Latics fight on All the latest West Ham news, features and opinion
Explore more:People: Matthew Upson, Neil Warnock, Robert Green, Robbie Keane, Harry Redknapp, Danny Gabbidon, Carlton Cole, Kieron Dyer, Wayne Bridge, David Sullivan, David Gold, Martin Allen, Steve McClaren, Chris Hughton, Sam Allardyce, Martin O'Neill Places: Cardiff, United Kingdom