Kane was expected to miss up to three weeks after injuring his left ankle on Dec. 7 against the Flames.
Hossa's injury is believed to be in his knee. It occurred during a collision in practice with Nick Boynton last month. Hossa told the media he would be a game-day decision, but minutes later Quenneville said he would not play.
"It's slow but it's progressing," Hossa said. "That's the main thing."
Corey Crawford will start in goal on Sunday against the Kings.
Jesse Rogers cover the Blackhawks for ESPNChicago.com.