The Panthers (44-30-8) went 18-5-2 in their final 25 games but finished one point behind the New Jersey Devils for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
Center John Tavares (New York Islanders), forwards Rick Nash (Boston Bruins), Evander Kane (San Jose Sharks) and James van Riemsdyk (Toronto Maple Leafs), and defensemen Mike Green (Detroit Red Wings) and John Carlson (Washington Capitals) are among the notable players who could become unrestricted free agents July 1.
"I would like another good player," Tallon said. "It doesn't matter. If they're more offensive, then that's fine too. I just don't like to pigeonhole what our need is. We're looking for good players, basically."
Tallon said he saw a need to improve offensively and defensively.
"We have a lot of good, young forwards coming as well," he said. "My preference would probably be both, but it depends on what it is, and who it is, and when it is. ... I would like to address both needs, possibly."
Panthers centers Aleksander Barkov, Vincent Trocheck and Nick Bjugstad, forward Jonathan Huberdeau and defenseman Aaron Ekblad are signed through at least the next three seasons.
Florida has two pending unrestricted free agents (forwards Radim Vrbata and Connor Brickley) and four restricted free agents (forwards Jared McCann and Frank Vatrano, and defensemen MacKenzie Weegar and Alexander Petrovic).
The Panthers were 19-22-6 on Jan. 25 and know that poor start cost them a chance at a playoff berth.
"We had a lot of good games where we deserved a better fate in the first half," Tallon said. "Probably inexperience cost us. We're looking for that not to happen again.
"It takes somebody with a little more experience, that's been through the playoffs before, that maybe helps us in the last minute of a period or important situations in games, and giving some confidence to our younger guys knowing that there's somebody in the locker room that's been through it before."
