The home side have plummeted down the standings in 2016 and are still searching for their first win of the year.
The Eagles remain the only team in the top four tiers who are yet to win a game in 2016, losing nine and drawing three since the turn of the year.
Including the end of last year, Alan Pardew's men have now gone 14 league games without tasting victory; they last went 15 matches without a league win in March 1998.
Last weekend they may not have won, but coming from behind to earn a point at high-flying West Ham United was a solid result. However, their lack of wins has them down to 16th and just seven points above the bottom three.
The Eagles' equaliser at the Boleyn Ground was tucked home by Dwight Gayle after Cheikhou Kouyate's red card for West Ham – which has since been rescinded – and the former is reportedly close to agreeing a new deal at Selhurst Park.
Palace's opener, meanwhile, was scored by Damien Delaney and a league-high nine of their Premier League goals this season have been scored by defenders, with five from Scott Dann, also a league-high figure for an individual defender.
The backline is doing well going forward, then, but Palace can't keep teams out having failed to keep a clean sheet in their last 12 league matches.
On home soil, the Eagles have now lost six Premier League games in a row. No team have lost seven home games in a row in the top flight since Wolverhampton Wanderers in April 2012 (nine consecutive games).
It is a busy month for Palace, with Saturday's game against Norwich followed by a visit from Everton on Wednesday. Pardew will be desperate to end the home woes in these two games before trips to Arsenal and Manchester United, which precede the huge FA Cup semi-final at Wembley against Watford on April 24.
That is five games in a fortnight for the out-of-form Eagles.
Recent Premier League form: LLDLLD
Recent form (all competitions): WDLWLD
The Canaries seem to be hitting form at just the right time and last weekend gave their chances of staying up a huge boost by beating fellow strugglers Newcastle United at the death.
It was a game they dominated for large periods, but Aleksandar Mitrovic's second-half double appeared to have denied them the win until the 93rd minute when Martin Olsson rifled home to send Carrow Road wild.
Norwich have taken seven points from a possible nine to move out of the drop zone and that is after managing just one from 27 available in their previous nine league games.
Victory tomorrow would be the first time since December 2012 that the Canaries have won three top-flight matches on the bounce.
Dieumerci Mbokani scored their second against the Magpies and appeared to inspire the frontline in his first match since getting caught up in the Brussels terror attacks. Norwich's three goals in that match are more than they managed in their previous five combined (two).
Despite their improved form of late, Norwich's tally of 31 points from 32 games is one fewer than they had at the same stage of the 2013-14 season when they were relegated.
They will be desperate to add to that total in their next two matches against fellow strugglers Palace and Sunderland, with three of their last four games against Arsenal, Manchester United and Everton.
Recent form: LLLDWW
Crystal Palace striker Connor Wickham was on red-hot form when he made it four goals in two matches on March 1, but he has been out since then with a thigh problem.
The former Ipswich Town striker could return here against Norwich, but if he is not deemed fully match-fit, then Emmanuel Adebayor could lead the line, although the Togolese is also doubtful with a knock.
Yohan Cabaye is also fit to return after missing last week's trip to West Ham.
Norwich captain Russell Martin is expected to be fit after a minor knock ruled him out of Newcastle's visit last Saturday.
The Canaries' only definite absentee is Alexander Tettey, who has a long-term ankle injury.
Palace possible starting lineup:
Hennessey; Ward, Dann, Delaney, Souare; Cabaye, Jedinak; Zaha, Puncheon, Bolasie; Wickham
Norwich possible starting lineup:
Ruddy; Wisdom, Bennett, Klose, Olsson; Jarvis, Howson, O'Neil, Brady; Naismith, Mbokani
Head To Head
Palace's 3-1 win over Norwich on the opening weekend of the season was their first victory over the Canaries in the Premier League having drawn four and lost four in their previous eight meetings
However, at Selhurst Park Norwich are winless in 14 league games, last winning there in May 1996 (D5 L9).
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We say: Palace 2-2 Norwich
Many will earmark this as a great chance for Palace to finally get a win, but Norwich are in fine form and will fancy getting at least a point.