Hjalmarsson hasn't played since Feb. 23 due to a suspected concussion and has been on the Hawks' three-game road trip and practicing with the team.
Meanwhile, Quenneville said captain Jonathan Toews, who will sit out his eighth game in a row with a suspected concussion, "had a good day off the ice (in Chicago). He worked and he's fine."
Quenneville added that the team is "hopeful that it's soon" that Toews begins skating before adding:"I can't give you a date. (Monday) was encouraging."
When asked if Toews' current condition had anything to do with his Feb. 23 car crash, Quenneville vehemently replied: "I don't think it has anything to do with where we're at."
One-timer: Ray Emery will make his third consecutive start in goal when the Hawks face the Blues. The veteran will be opposed by Jaroslav Halak.