The Eagles have been setting unwanted records throughout the opening weeks of the season and they are still yet to register a point or a goal in the Premier League this term.
Next up for Palace is a home game against defending champions Chelsea and they do not boast an impressive home record against the Blues, as they have only won one of their last seven matches against their London rivals at Selhurst Park.
Hodgson's men are already five points adrift of safety, but they should be able to welcome back influential winger Wilfried Zaha, who has been out with a knee injury since the opening weekend of the season.
Chelsea will head into the contest looking to bounce back from their 1-0 home defeat to Manchester City before the international break, a result that leaves Antonio Conte's side six points off the pace at the top of the standings.
The Blues have performed better away than they have at home this season, as they are yet to taste defeat on the road, while they have also won on each of their last three visits to Palace.
The defending champions do have injury concerns ahead of the match, as N'Golo Kante has been ruled out for three weeks with a hamstring injury, while Alvaro Morata is absent with a similar issue, although he could be fit for Wednesday's Champions League clash with Roma at Stamford Bridge.