"I hope to be back here, we obviously have unfinished business," Stamkos said one day after the Lightning season ended with a 2-1 loss to the Pittsburgh Penguins in Game 7 of the Eastern Conference Final. "This group had been unbelievable. This city has been unbelievable. I can't believe it's been eight years already."

TAMPA -- Steven Stamkos said Friday he wants to stay with the Tampa Bay Lightning rather than sign elsewhere as a free agent.

Stamkos played in Game 7, his first since March 31 after he was sidelined by a blood clot near his right collarbone.

The 26-year-old center can become an unrestricted free agent on July 1. He and the Lightning have been attempting to come to terms on a long-term contract since before this season began. He said he has not thought much about his status and will resume the process after a short rest.

"I haven't thought about anything other than the playoffs," Stamkos said. "I'm going to rest for a week or two and then we'll start looking at things. It's not as easy as everyone thinks it is. There are certain cases where it works out right away and cases where it takes longer."

General manager Steve Yzerman said Friday the Lightning want to sign Stamkos and said the last conversation he had with his agents was before the NHL Trade Deadline, which was Feb. 29.

"My preference is for him to come back," Yzerman said. "That's [Stamkos'] decision. It is out of my control. He is an unrestricted free agent on July 1 and I can't force him to sign a contract with us if he doesn't want to."

Earlier this season, Elliotte Friedman of "Hockey Night in Canada" reported that the Lightning offered Stamkos an eight-year contract with an average annual value of $8.5 million ($69 million total).

Chicago Blackhawks forwards Patrick Kane and Jonathan Toews each signed an eight-year, $84 million extension in July 2014, when each had one season left on his contract. Los Angeles Kings center Anze Kopitar signed an eight-year contract reportedly worth $80 million during this season.

Stamkos said there's been no pressure from the NHL Players' Association suggesting he look for a more lucrative deal.

"Where does that come from?" Stamkos said. "I've seen it out that and there is zero talk between the Players' Association about that."

Stamkos said so far the sides have kept their word about keeping contract discussions out of the media.

"We've all kept all that stuff internal and I expect things to stay that way until a decision is made," Stamkos said. "My preference is to stay here, and if both sides want to make that happen, it'll happen."

The No. 1 pick of the 2008 NHL Draft by Tampa Bay, Stamkos has 562 points (312 goals, 250 assists) in 569 regular-season games. He won the Rocket Richard Trophy in 2010 and 2012, has four 40-goal seasons, and scored at least 20 in his first eight seasons in the NHL. He had 64 points (36 goals, 28 assists) in 77 games this season.

In 2011-12, he became the 20th player in NHL history to score 60 goals in a season. He has been Lightning captain since March 6, 2014.

"When the organization drafted Steven Stamkos, it put the franchise back on the map," Lightning coach Jon Cooper said. "He's a superstar player in the League who has scored 300 goals. Do I want him back? Yes, but that's not a question for me, that's a question for [Stamkos]."

The Lightning have other contract issues to consider. Forward Nikita Kucherov will become a restricted free agent on July 1, and defenseman Victor Hedman and goalie Ben Bishop each has next season remaining on his contract.

"The future of this organization for the next seven or eight years will be determined by what happens in the next two summers," Yzerman said. "We have to be careful. Every contract we offer will affect other contracts."