According to the Liverpool Echo, the Brazilian international was in line to make his competitive debut for the Reds on Sunday, but has been unable to shake off a knock picked up during his side's friendly win over Torino earlier in the week.
Further concerns were raised earlier, when Fabinho was pictured leaving the training ground alongside the club doctor Andrew Massey.
Klopp is now likely to turn to Jordan Henderson to anchor the midfield on Sunday, despite only recently returning to training following a gruelling World Cup campaign with England. However, Fabinho hasn't yet been ruled out of contention, and it is likely that the club's medical team will continue to assess him over the next 48 hours before making a decision.
Liverpool fans will be eager to see their new signings in action against the Hammers, after a highly successful summer transfer window for manager Jürgen Klopp. The charismatic coach has signed a host of new stars, including the likes of Brazilian number one Alisson, midfield star Naby Keïta, and experienced winger Xherdan Shaqiri.
Meanwhile, the Reds have reportedly missed out on the chance to sign Lyon midfielder Nabil Fekir, with a number of sources suggesting that it's too late for the Merseyside club to pull off a deal.
Despite having a move to Anfield break down earlier in the window, Liverpool were still believed to be keen to re-attempt the move, but their hopes now appear to be over.