The Reds have already recorded six points more than they had in the whole of last term and are out to add to their impressive run of just one home league defeat this season.
Jurgen Klopp is looking to make it three wins out of three against Palace, but is well aware of the threat posed by the former Liverpool striker Christian Benteke, who has scored three times against the Reds in his last two appearances at Anfield as an opponent.
The home side have defensive issues heading into the game, with doubts over Ragnar Klavan, Luscas Leiva and Joel Matip. Joe Gomez is back available after injury and could come into contention for a start, but England duo Jordan Henderson and Adam Lallana are still sidelined.
Palace meanwhile, are still not certain of staying in the division despite their recent upturn in form and a defeat would keep them in the relegation dogfight.
One major factor in their good run has been the loan signing of Mamadou Sakho from Liverpool, who won't be available against his parent club.
With Sakho absent, Allardyce – who has never won as a manager at Anfield - is expected to hand a start to the fit-again James Tomkins.
Palace will also be able to call upon Loic Remy and James McArthur, with the pair also back to full fitness.