If the Coyotes don't sign Bleackley, they will receive a supplemental second-round pick in the 2016 draft.
Bleackley had 46 points (13 goals, 33 assists) in 55 games with Red Deer of the Western Hockey League this season.
"My agent has a close relationship with [Arizona general manager John Chayka] and they still have time to sign me," Bleackley told the Red Deer website. "I'm not expecting anything.
"My job, whether I get signed or go back into the draft or whatever happens, hasn't changed and won't change. I'll work hard every day and first and foremost get back from this injury and then train in the summer."
Bleackley has not played since March 19 because of a wrist injury sustained when a skate blade severed tendons during the first period of a win against Edmonton. It was his second major injury of the season; he missed six weeks because of a broken left kneecap sustained Jan. 23.
The wrist injury was expected to keep him out for the remainder of the season, but Bleackley could play for Red Deer during the Memorial Cup, which begins Thursday and runs through May 29. Red Deer is hosting the tournament at Enmax Centrium, and will play its first game against Ontario Hockey League champion London on Friday.
Bleackley said he is taking a wait-and-see approach playing in the tournament. He returned to practice last week and has been participating in on-ice workouts.
"It's still kind of doubtful, but I think for me right now, it's about what I can do to help the team," he said Monday. "Going to practice and skating and just being around the guys as much as I can and helping any way I can is just what I'm doing. And that's all I can do right now. But we'll see."
Red Deer coach Brent Sutter said he doesn't believe Bleackley will be able to play.
"I don't know what the chances are," Sutter told the Red Deer website. "He's been practicing the last two days and we'll see how it goes, but it's not something that I'm optimistic about. I'm still going off of what the surgeon said who performed the operation."
Bleackley said his focus now is on the Memorial Cup, not what might happen later.
"If that does happen [re-entering the draft], I think two teams would have made mistakes," he told the Calgary Herald. "Whether I'm taken in the fourth round, fifth, seventh, not at all, or in the first round, my job doesn't change. That's to be a hockey player. I feel like I've got a lot left to give. A lot of people may have counted me out already … but you won't be able to convince me otherwise until it's all said and done.
"I was taken where I was for a reason. I believe that to this day. We'll see where the future goes."
