The Dallas Stars forward won't know for a while whether his health will allow him to continue his career.
Peverley said Friday his recovery is "going to take time" in his first meeting with reporters since collapsing on the bench during a game March 10 because of an irregular heartbeat.
The 31-year-old Peverley said he skated Thursday for the first time since the incident. That was 10 days after he underwent a procedure in Cleveland designed to correct his condition. He won't play again this season.
"The recovery process is going to take time and as cliche as it sounds, I've really learned this in the past week that it is day by day," Peverley said at a news conference before the Stars' game against Nashville. "Ultimately my goal would be to come back if it's the right time."
Peverley said he remembered everything from before and after he lost consciousness against Columbus. The game was postponed and will be played April 9.
The understated veteran didn't offer a dramatic re-enactment of the critical moments when his life was in danger. He simply said he remembered "feeling like kind of like almost like I was seizing up a little bit," and leaving it at that.
After he collapsed, Peverley was rushed to a nearby hallway, where he was quickly stabilized before going to a hospital.
"I don't want to say I keep replaying it in my head but sometimes you think about it," Peverley said.
Peverley can't go through any contact drills until he's finished with blood thinners required by the procedure, which Dimeff said takes about a month.
"We're really just ramping up his exercise activity slowly and monitoring him closely at this point," Dimeff said.
Peverley said his wife supports what he wants to do and it'll be a while before they seriously discuss his future in the sport.
"I think it is traumatic for the family, I think having that possibility of me not being around," said Peverley, who has two young children. "I was very lucky that the NHL and all the doctors and all the trainers were very prepared because they did save my life."
Although he won a Stanley Cup with Boston in 2011 and has played 442 games over eight seasons, Peverley's never been in a spotlight quite like the one he was in after the collapse.
Dallas teammates and their families brought meals for days after he got out of the hospital and he said he's heard from "so many teams and people I don't even know." He didn't want to say he hated the spotlight, but he was hoping Friday's session would put the issue to rest.
"I feel horrible for the team," Peverley said. "I don't want this to be a sideshow. They're going for the playoffs. They're only a few points out. The focus should be on them and them trying to make the playoffs for the city."