The Premier League club are struggling to secure the talent they need to bolster their squad and avoid relegation.
“I can't give any update in regard to any player, but [sporting director] Doug Freedman and [chairman] Steve Parish are working hard to try to bring a couple of players at least into the club," Hodgson said to reporters.
“Until such a time as there is something concrete to say, I'm better off saying nothing.
“For a long time all throughout this window — even in the summer — we discussed certain areas where we thought it would be good to get strength into our squad.
“The loss of Cheick Doucoure [to a season-ending ACL injury] has exacerbated that situation. No doubt the central midfield position is something we need to look at and strengthen.
"One or two other positions as well we've always liked and thought we could do something but it's difficult.
“January is probably the hardest one of all. I can only back Steve Parish, Doug Freedman and other investors in what they're doing and hope that, come February 1, there might be one or two surprises."