A win could see the Reds go just three points off fourth spot, providing results elsewhere go in their favour, such as City losing their game at home to Aston Villa the day before.
Palace have been a bit of a bogey side for Liverpool in recent years, with the Eagles winning the last three games between the two sides - including a 2-1 win at Anfield earlier this season.
However, Alan Pardew’s men have been struggling recently, after a great start to the season and sit just nine points above the relegation zone having taken only four points from their last 12 league games.
Jürgen Klopp rested several key men in midweek, with Philippe Coutinho and Daniel Sturridge both not making an appearance.
Both are in contention to start on Sunday, but Klopp may opt to stick with the team that did so well against City.
Mamadou Sakho trained this week ahead of the game and will be available for the game, after not making an appearance against City.
However, Lucas Leiva will play no part after it was revealed he would be out for around six weeks with a thigh injury.
For Palace, Connor Wickham has found some form by scoring four times in his last two games, but is a doubt with a knock, along with goalkeeper Wayne Hennessey.
Jason Puncheon and James McArthur will also miss the game, but full-back Pape Souare will be available after coming back from suspension.
Crystal Palace had a great start to the season, with many thinking they could even sneak into a European spot with them sitting a few points outside the top-four at Christmas.
However, Palace have failed to win in their last 11 games and have yet to win in this calendar year, seeing them freefall down the league into 14th.
They are on 33 points and a win would ease the nerve of most Palace fans, with relegation quickly becoming a possibility - albeit an unlikely one - because of their poor form.
In the last six meetings between the sides, Palace have lost just once and have won four times.
Liverpool's last win at Selhurst Park came all the way back in 1997.
The Eagles have also managed to score 11 times against the Reds, during the last four matches between the two sides.