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Stamkos is in the final season of his five-year, $37.5million contract he signed with the Lightning in July 2011.
The 26-year-old has a no-movement clause in his contract and is scheduled to become an unrestricted free agent on July 1.
And Yzerman issued a statement on Monday regarding the star centre, insisting the team have no intention of trading Stamkos before the NHL's upcoming trade deadline on February 29.
"As February 29th approaches, I am stating today that Steven Stamkos will not be traded before the NHL's trade deadline," Yzerman said.
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"I have said repeatedly that it is our hope to reach an agreement with Steven on a new contract at some point, and with 27 games remaining in the season, our entire organization, Steven included, wants to focus on making the playoffs.
"I will keep the negotiating process strictly between the involved parties and have no further comment on the state of those negotiations."
Stamkos had expressed during the All-Star break that he hoped to remain in Tampa Bay for the rest of the season.
"My view hasn't changed. I want to win with Tampa," Stamkos told ESPN.
"I don't think that's going to change between now and 30 days from now."
The Lightning, who hold one of two Eastern Conference wild-card spots, will hang on to Stamkos as the team aims to return to the Stanley Cup Final.
Stamkos ranks second on the team with 42 points behind forward Nikita Kucherov (48).