The east London outfit currently languish at the bottom of the Barclays Premier League after a four-game losing streak brought a sudden end to a mini-revival.
Up in arms: Grant has leapt to the defence of his Hammers squad after harsh words from co-owner Sullivan
West Ham's form led to comments from Sullivan the club have a '25% chance' of staying up and are 'likely to be in the Championship next year.'
The Hammers have a mere four games to drag themselves away from the precipice and face a tough trip to Manchester City on Sunday.
Despite this, Grant believes West Ham can pick up the points that will secure survival and refuted Sullivan's comments.
'I didn't read it so I can't tell you [everything] but David is a businessman.
'I think we have a chance to stay up. We are two points from the place that will keep us in the Premier League and of course we can do it.
'We showed that even we had less chances before we played well and took points.
'Now we have four games to the end of the season and I don't know how the chances are by percent, I am not a businessman.
'What I can tell you, though, is that we have a good chance to stay and we will do everything to do it.'
Hard line: Sullivan had questioned the Hammers squad ahead of their relegation scrap
Grant believes his charges need nine points to secure survival but admits seven points could be enough.
However, the former Chelsea and Portsmouth boss refused to put a percentage on their survival chances.
'If I say to you now there is a 51% or 32.5% chance it doesn't matter.
'It only matters in money because if he wants to give 25% more to the players if they stay in the league, it is okay.
'If you put the chances of us staying up four months ago the chances were 10%, so it always changes.
'If we take four points from the next two games the chances will be more than [the current figure] and it will continue like this until the end of the season.'
Hammer blow: Torres opened his Chelsea account against West Ham condemning Grant's side to a 3-0 loss
Last weekend Grant's side were beaten 3-0 at Stamford Bridge and now face a trip to Eastlands without key players such as Scott Parker, Mark Noble, Gary O'Neil and Wayne Bridge.
The quartet have been some of West Ham's key performers this season, while several other players have seemingly failed to live up their billing.
Such performances led Sullivan to question whether the players care enough but Grant does not necessarily agree with the view.
'I don't think so. I didn't read the article so I need to read it because sometimes it is translated not so good by the media.
High praise: Parker has been the exception to the rule
'But I can speak only about what I see. I could say yesterday, against Chelsea last weekend and the games before that the players are giving everything.
'Of course we can ask for more in quality but they are giving everything and the spirit is good.'
While Grant disagreed with several ofhis co-chairman's sentiments, the Israeli manager did echo Sullivan's comments on the Hammers fans.
Sullivan said he felt sorry for the West Ham supporters and felt they had failed to deliver this season.
'WestHam is a massive club and part of our vision is to stop fighting against relegation because West Ham did it too much in the last years and also this season.
'This season we knew it would be difficult but of course we didn't want to be in this place so we feel for the supporters.
'We are doing everything for them to feel good and I think even the supporters know the players give anything.
'They are behind us and if you saw the last game against Chelsea you heard them more than we heard the Chelsea supporters.'
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