Hossa returned to Chicago over the weekend because of a family matter and sat out the team's game against the Vancouver Canucks on Saturday. Quenneville said he expects to be without Hossa again against the Edmonton Oilers on Monday.
"I don't think we're going to have him tonight," Quenneville said on the "Coach Q Show" on WGN-AM 720 on Monday morning. "We expect him the rest of the trip, though."
The Blackhawks are entering their fourth game of a seven-game road trip. They are 2-1 on the trip.
Hossa has 10 goals and seven assists in 20 games this season. He returned to the Blackhawks' lineup Thursday against the Winnipeg Jets after missing the previous three games with a lower-body injury.