Stone, 26, had surgery to repair torn anterior cruciate and medial collateral ligaments in his left knee. He is skating but has not been cleared to practice. The Coyotes open this season against the Philadelphia Flyers at Gila River Arena on Oct. 15.
Last season, Stone had six goals and 36 points in 75 games for the Coyotes.
Chayka confirmed forward Dave Bolland failed his physical and will be placed on long-term injured reserve.
Bolland, who was acquired from the Florida Panthers with Lawson Crouse in a trade for two future draft picks on Aug. 25, has been recovering from an ankle injury that has limited him to 78 games over the past two seasons.
Coyotes defenseman Kevin Connauton sustained a lower-body injury during an informal workout at Arizona's practice facility in Scottsdale prior to training camp and won't be on the ice when camp opens Friday.
Chayka said the injury isn't considered long-term. Connauton had nine points in 38 games for the Coyotes last season after being claimed off waivers from the Columbus Blue Jackets.
"It happened at an informal skate. [It was] kind of an unfortunate accident, but I don't think he'll be out for too long," Chayka said. "He's going through the rehab process and won't be here for the start of camp, but hopefully he'll be up and running soon.
"He should be fine as it relates to the regular season for sure."
