With the "negotiation period" open for free agents, Sabres GM Tim Murray told reporters on Saturday he's ready to go after the "big fish" in free agency.
"The next conversation I plan on having with (Newport Sports Management) is ask if Steven is going to be available on July 1 and if he has an interest in Buffalo," Murray said. "I have to ask that question or I wouldn't be doing my job if I didn't."
Several Sabres players, including center Ryan O'Reilly, are represented by the same agency.
Stamkos missed the last month of the season after surgery to remove a blood clot. He returned to action and played just one game in the postseason as the Lightning were knocked out by the eventual Stanley Cup Champion Penguins in the Eastern Conference Final.
Reports indicate Stamkos could fetch as much as $12 million per year.
Murray also added he spoke with the agents of Jimmy Vesey. Buffalo traded one of their third round picks to Nashville in exchange for the exclusive rights to negotiate with the Harvard star.
"(Vesey) said good luck with the draft and we'd touch base again next week," Murray said.
The Sabres have until August 15 to sign Vesey or he'll become an unrestricted free agent and will be able to sign with any team.