The 25-year-old has been in the treatment room since hurting his ankle in the league clash with Huddersfield Town two weeks back.
Although the utility man had a scan to ascertain the degree of the injury, Palace have given out little about the player's expected layoff period.
"We were very disappointed to lose Jeffrey Schlupp in the last game [against Huddersfield], as he was out for a long time after the Brighton injury and did so well to get back," Hodgson said at a press conference ahead of Saturday's home tie.
"So we are disappointed to lose him again, and we still have doubts on James Tomkins and Alexander Sorloth, so we’ll check them tomorrow but they are very much doubts.
"Luckily all others reported back.”
The recent setback was a massive blow for Schlupp, who only returned from injury the week before, after almost two months on the sidelines.
The Black Star had been a key feature of Hodgson's set-up since the former England manager replaced Frank de Boer in September.
The German-born, who joined The Eagles from Leicester City in January last year, has made 22 Premier League appearances, involving 21 starts, so far this season.