Palace, whose injury list includes Joel Ward, Scott Dann, Ruben Loftus-Cheek and Jason Puncheon, suffered a further blow in their FA Cup defeat to Brighton in which Jeffrey Schlupp and Andros Townsend were injured.
Hodgson's fresh additions to those on the sidelines means that the Eagles are without almost an entire starting lineup, but the 70-year-old has insisted that the club are working to provide backup.
"We are not having many transfers confirmed in this window," Hodgson told the Evening Standard. "The one thing we know for certain is that the agents out there are working 24-7 and the clubs, many like ourselves, are working very hard to find an answer to areas to where we need reinforcements.
"It is interesting to see that very few transfers seem to have been actually nailed down in the middle of January. What actually happens at the end of it in terms of what players arrive here - if any - is another question altogether.
" have sketched out the profiles, we have identified the areas where we would like some players to come in. [The] big question [is], are we going to find them? That is not just Crystal Palace asking that question, it is probably everyone from the top three or four downwards."
Palace play Burnley at Selhurst Park on Saturday afternoon looking to build on a decent run of Premier League form.