The Eagles have eased their relegation worries in recent weeks by picking up five wins and a draw in their last seven outings, a run that includes wins over both Chelsea and Arsenal.
Allardyce has now targeted another major scalp when Palace head to Merseyside this weekend, a week on from a 2-2 draw with Leicester City, and the former England manager has been boosted by the return to action of Loic Remy and James Tomkins.
"If we're as clinical as we were against Arsenal and Chelsea, and don't make basic mistakes like against Leicester - we have a chance," he told reporters.
"Loic and defender James are back in the squad, which is good to see with such a congested week coming along. We'll need it over the seven days. Obviously Mamadou Sakho can't play, so it's important that James is back. James McArthur is also back and so is Patrick van Aanholt."
Palace are currently 15th in the Premier League table, seven points clear of Swansea City in the final relegation spot with a game in hand to play.