"We're trying to get something done [with Stephen]," Tallon told the Panthers website. "You get one shot at it, being an unrestricted free agent and we're trying to do the best we can for both parties. If I can come up with the right number, and it works out, that's fine. I think we'll go through [Sunday] and then we'll work on that ... and make a decision early next week."
Weiss was limited to 17 games in 2012-13 due to injury. He had a goal and three assists.
The No. 4 pick in the 2001 NHL Draft, Weiss, 30, has played all of his 654 NHL games for the Panthers. He has 145 goals and 249 assists (394 points).
He played in the Stanley Cup Playoffs for the first time in 2012, scoring three goals and two assists in a seven-game first-round loss to the New Jersey Devils.
Tallon said the team would have interest in Lecavalier, who will become a free agent when the Tampa Bay Lightning complete their compliance buyout of his contract.
"Very interesting," Tallon said. "His leadership, his skill level; we've got young, big centermen that would learn a lot from him, so, yeah, we have some interest. Hopefully he has some interest as well."