Grant looked to be on his way out of Upton Park in January after rumours linked Martin O'Neill with the Israeli's position, but he remained in charge and seemed destined to keep his post after overseeing a four-match unbeaten run to move the club out of the relegation zone.
But a recent five-match losing streak has seen the club plummet to the foot of the table and they are now three points adrift of safety with three games remaining.
'Lazy': Avram Grant's (left) job is in doubt due to his players, according to Julian Dicks
While vice-captain Scott Parker has excelled in the middle of the park, picking up the Player of the Year award from the Football Writers' Association, few of his team-mates have stepped up to the plate this year.
The Hammers have conceded an average of two a game away from home this year while goals have been hard to come by at the other end.
Dicks admits the manager must bear overall responsibility for the dismal season, but maintains that West Ham would not be in such a perilous situation had a number of the club's players put in the required effort.
'The last three games are about the players now. The players have to stand up and be counted. They are all on good money and it's about time that they started to earn it, and that hasn't been the case with some of them this season,' Dicks said.
Player of the Year: Scott Parker has been in fine form all season
'There's a few players who are there that aren't good enough. That's not their fault, but there are some players there who are good enough that don't work hard enough.
'Robert Green has pulled off some world-class saves this year, Scotty Parker has played well, so has (Mark) Noble, and I like Demba Ba and Robbie Keane, but once you get past those, then you struggle to put your hand on anyone else.
'If the players don't have passion and desire then you are going to struggle to win games so it's down to Grant or whoever is in charge to get rid of these players.'
Dicks, who made over 300 appearances for the east London club, admires the way that Grant has stuck to his task of trying to keep the Hammers up despite all the speculation surrounding his future.
'World class saves': Dicks has been impressed by Robert Green
The former West Ham and Liverpool defender admits that the ex-Chelsea boss will have to leave his post if the club go down, though.
'I think he has gone about his job particularly well given the amount of stuff that has come out about him,' Dicks added.
'He has kept his dignity really well but football is a results-based game and if he is not getting the results then someone else has to come in and try to get results. If a team goes down then the manager usually goes and I don't see it being any different at West Ham.'
Parker has missed the last three games due to an Achilles injury but it is hoped that he will be available for the club's remaining fixtures against Blackburn, Wigan and Sunderland.
Heart of Iron: Dicks (left) in his playing days
The England midfielder will undoubtedly be the subject of numerous offers this summer if West Ham are relegated, but Dicks thinks the club should not be pressured into selling their prized asset.He said: 'It's down to the club if they want to sell him or not. He's under contract. They can make him stay.
'If they want ?10million for him then they should hold out for ?10million. If it happens, it happens, and if it doesn't then he stays at West Ham.'
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