Hossa was injured during the first period against the Colorado Avalanche on March 18 and has not played since. He missed Wednesday's game against the Anaheim Ducks.
Quenneville said Hossa's injury isn't long term.
"He's doing all right," Quenneville said after practice at Johnny's IceHouse West. "Hopefully, he'll get on the ice (for practice) on Sunday. He's progressing. … With him, not likely (to play on Monday.)"
Hossa has 13 goals and 10 assists in 28 games this season.
Blackhawks forward Patrick Kane has picked up most of Hossa's minutes in his absence. Kane double-shifted throughout Wednesday's game and played a team-high 24:23.
Quenneville said utilizing Kane in the same way could be a possibility again on Monday.
"At least you can go through that in games, maybe see how the game is going," Quenneville said. "It's a great option to have. I think maybe we'll put someone up there to start."