Never mind their current iTunes revival, The Beatles were at number one the first time around with She Loves You the last time the Hammers won at Anfield in 1963.
Grant also faces being without inspirational midfielder Scott Parker, who is struggling with a chest infection.
Hoodoo: West Ham have not won at Anfield since 1963, and Avram Grant will be praying for a miracle
But despite his side lying bottom of the Barclays Premier League with just one win all season, the former Chelsea and Portsmouth chief was this week told his job is safe by vice-chairman Karren Brady.
And Grant insists he is not feeling the heat as he bids to end the Hammers' Kop hoodoo tomorrow evening.
'We need to deal with the pressure. I don't think you can be in football without pressure,' he said.
'It's good to know everybody shares the vision of the club even at this difficult time. Of course there are areas we want to improve.
'What's important for me is the team. I'm not the issue at the moment, I need to do my job for the team.'
Coupled with their wretched record at Anfield, West Ham are also without a win on the road since the beginning of last season.
Struggling: Key player Scott Parker is doubtful for the Liverpool match - he has a chest infection
Three successive draws against Birmingham, West Brom and Blackpool could not lift them off the foot of the table but Grant is confident the elusive away victory will come.
'It's always not easy to play at Anfield, especially when Liverpool need the points,' he added.
'But we have lost just twice in 11 games, we want to continue with that and a little bit more. If we continue to do the right things - and there are things we could do better - the win will come and we will do everything to get it tomorrow.'
One crumb of comfort for Grant is the absence of Liverpool captain Steven Gerrard, so often the scourge of West Ham down the years, after the midfielder was injured playing for England in midweek.
Reds boss Roy Hodgson is unhappy Gerrard stayed on the field for 85 minutes of the friendly defeat by France when he was only due to play an hour.
And former Israel coach Grant knows how Hodgson feels after his star summer signing, Thomas Hitzlsperger, was hurt playing a friendly for Germany in August and will not be fit until February.
'I have experience of that,' he said.
'Thomas was injured playing for Germany three days before the season started. He was in very good condition and then he played more than 60 minutes which was not so good.
'But I was a national coach for four years so I know the problems for both sides. Everybody has to understand when there is a friendly you have to think twice.
'Things like that happen in football but I would prefer if it happened in the league, not in a friendly international.
'Gerrard is a very good player but Liverpool are a very good team anyway, so we will have a difficult game.'
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Explore more:People: Karren Brady, Thomas Hitzlsperger, Roy Hodgson, Steven Gerrard Places: Chelsea, Birmingham, Liverpool, Israel, France, Germany, United Kingdom