"I hope so," Stamkos said to TSN of another 60-goal season. "I'm definitely not going to tell myself it's not [possible]. That's something that was a very special time in my career; hopefully I get a chance to do it again.
"I have done that before; I haven't won a Stanley Cup before. So that's the main priority."
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Stamkos, who scored 60 goals in 2011-12, his last full season, this week has been telling the media how confident he is the Lightning can build off their first-round exit from the Stanley Cup Playoffs this season.
"We have a good thing going down in Tampa," Stamkos told The Canadian Press on Wednesday. "We have a great owner, we've got a great GM in Steve Yzerman, and we've got a good young team. I want to win, and hopefully I can do it in Tampa."
Stamkos said the additions of free-agent center Brian Boyle and defenseman Anton Stralman, and the re-signing of forward Ryan Callahan improved the Lightning, who were swept in the Eastern Conference First Round by the Montreal Canadiens after placing second in the Atlantic Division.
"We didn’t have the finish we wanted to last year, but with the new faces coming in, the expectations are probably set a little higher," he said.
Stamkos, 24, will begin his first full season as captain after being limited to 37 games and 25 goals in 2013-14 because of a broken leg. He told "Total Hockey" he started his summer workouts with Gary Roberts earlier than usual.
"The leg's great; I couldn't be more pleased with how it's coming along," Stamkos told TSN.
After forwards Jonathan Toews and Patrick Kane each signed an eight-year, $84 million contract to stay with the Chicago Blackhawks, Stamkos has often been mentioned as next in line for a similar big deal. He has two seasons remaining on a five-year, $37.5 million contract he signed in 2011.
"[Free agency] is something that is kind of on the backburner right now, with the injury and trying to focus on the year and get back to being the player I know I can be," Stamkos told TSN. "That's kind of the first priority.
"I will say this: I definitely enjoy playing in Tampa. The ownership group has been unbelievable; it's an unbelievable place to live and play, and the fans are great, and we have a competitive team. And for me, I want to win. I want to give myself the best chance to win, and right now for me that's Tampa, so I'm looking forward to this year."