"I'm trying to take the steps one at a time and just see what happens," Peverley told Mike Heika of The Dallas Morning News in comments published Wednesday. "If I can play, that will be great. If I can't, then I'll deal with that at that time."
Peverley collapsed March 10 during a game against the Columbus Blue Jackets at American Airlines Center in Dallas. He had been diagnosed with and underwent an initial procedure for an irregular heartbeat during the preseason and had a second procedure nine days after he collapsed at the bench.
He said he's been increasing his workouts and raising his heart rate.
"I've been able to do more and use my upper body, so I definitely feel I'm making progress," he said. "But it's just the start. I have a long way to go."
Peverley will be among the presenters at the 2014 NHL Awards in Las Vegas on Tuesday (7 p.m. ET; NBCSN, CBC). He will be part of the presentation group for the Bill Masterton Memorial Trophy, awarded to the player who best exemplifies perseverance, sportsmanship and dedication to hockey.
"I think the fact that Bill Masterton was a member of the North Stars and the Stars organization, I do like the fact that I get to help represent that history for the team," Peverley said. "And I like the award and what it stands for, and I think that knowing the stories of the nominees and presenting the trophy to the winner, that could be motivation for me to come back, if coming back is possible."
Peverley, who turns 32 on July 8, had seven goals and 23 assists in 62 games with Dallas in 2013-14. He has 84 goals and 157 assists in 442 games with the Stars, Boston Bruins, Atlanta Thrashers and Nashville Predators.