Shaw missed the final five games of the Blackhawks' second-round series with the Minnesota Wild after he was injured in Game 1 on May 2.
"[He] certainly adds an ingredient you appreciate as a coach and a teammate," Quenneville said after practice on Thursday. "Has that relentless competitiveness, some skill offensive and he’s hard to play against. Nice set of hands, can take faceoffs, play center, wing. You look forward to getting him back. We expect to have him back on the ice this weekend and we’ll get a better determination of when he’ll play."
Shaw has two goals, two assists and a zero rating, and has averaged 15:54 of ice time in seven playoff games this season. He had 20 goals, 19 assists and a plus-12 rating in 80 regular-season games.
The Blackhawks will play the winner of the Los Angeles Kings-Anaheim Ducks series in the Western Conference finals. The Kings and Ducks will decide their series in Game 7 on Friday. The Western Conference finals begin Sunday.