Price, whose inspired play during the playoffs helped guide the Canadiens to the Cup Final for the first time since 1993, was expected to need 10-12 weeks to recover from the knee procedure. The 34-year-old also sustained a hip injury during the post-season, but that did not require surgery.
"He just arrived in Montreal not too long ago," Ducharme said at his charity golf tournament at the Club de Golf de Joliette. "I'll have more news next week, and he should be there for the start of camp, and if not at the start, very soon after that."
Price was 13-9 with a 2.28 goals-against average, a .924 save percentage and one shutout in the Stanley Cup Playoffs.
Amid a transformative off-season for the Canadiens that saw them lose captain Shea Weber, whose career is on hold as he navigates multiple injuries, there was a chance Price could be lost, too.
The Canadiens left Price unprotected in the 2021 NHL Expansion Draft, meaning the Seattle Kraken could have taken the goalie who has tended Montreal's crease for his entire 14-year career.
"I was never nervous," Ducharme said. "We knew it was a possibility we could lose Carey but it was the organization's decision, and they had evaluated every situation and the reasons they believed he would stay with us."
Jonathan Drouin, who took a leave of absence from the Canadiens in April and hasn't played since, is also expected to be at training camp. In 44 games last season, he scored twice and assisted on 21 others.
The 26-year-old, along with Mathieu Perreault, Josh Anderson and Laurent Dauphin took part in Ducharme's golf tournament.
"He's going really well," Ducharme said of Drouin. "He's been in Brossard working out getting ready for the season for a few weeks now. He kept in touch with the players all along, and they did too because they care. He's a good guy, the guys love him, and even though he was not with us, he was still part of it because the guys were close to him.
"So it's all about himself right now, and taking care of himself, getting ready physically and mentally. Every time I spoke to him, I find he's in a good spot. He's relaxed, he's in good shape, he's confident and he's excited. He wants to come back and show who he can be."
The Canadiens' first pre-season game is Sept. 25, in an Original Six matchup with the Toronto Maple Leafs. Montreal opens the regular season by visiting Toronto on Oct. 13.