On Tuesday, Peter Luukko, the club president, said the Flyers were "blockbustered out" when asked about Stamkos' playing for the Orange and Black.
Stamkos, 21, has an NHL-best 96 goals over the last two seasons. This season, he helped Tampa Bay reach the Eastern Conference finals, where it lost to Boston in seven grueling games.
"Unless the Flyers offer something ridiculous, like $12 million [a year], the Lightning will never let him go," said someone with knowledge of the negotiations.
In the unlikely event that Tampa Bay did not match an offer, the Flyers would have to give the Lightning four No. 1 picks - and probably would have to deal two veterans to open salary-cap space on an already-revamped roster.
Don Meehan, Stamkos' agent, met with Yzerman on Wednesday. They plan to meet again on Thursday and work toward reaching middle ground, Yzerman told the St. Petersburg Times.
"All I would just say is that, as far as the salary cap and cash, we're in a position to do whatever is right for the organization," Yzerman told the newspaper.
The Flyers, meanwhile, are preparing for Friday's opening of the free-agent market, one that is expected to include several forwards on their radar, including Erik Cole, Jamie Langenbrunner, Michael Ryder, Michal Handzus, and Simon Gagne. The latter two players are former Flyers.
"The first thing we're looking for is a gritty guy who is a good leader in the room," said one Flyers source.
Contact staff writer Sam Carchidi at scarchidi@phillynews.com
or on Twitter at BroadStBull.
