Alex Killorn of the Tampa Bay Lightning looks on prior...

Alex Killorn of the Tampa Bay Lightning looks on prior to Game Three of the Eastern Conference Final against the Pittsburgh Penguins during the 2016 NHL Stanley Cup Playoffs at Amalie Arena on May 18, 2016 in Tampa, Florida. Credit: Getty Images / Mike Carlson

Traditionally, June is the month before the storm of moves hits the NHL. But this June could be very different, particularly for the Islanders.

General manager Garth Snow’s team will look different next season for sure, even if he doesn’t add a single player from outside. Kyle Okposo and Matt Martin are headed for free agency on July 1 and contracts elsewhere. Sources indicate that there have been no talks between either player’s agent and the Isles since the season ended.

Preliminary talks on a new deal have begun with Frans Nielsen, but those are in the early stages. He too could be out the door on July 1.

The crop of top-level free agents is thin. So June, with the potential for contract buyouts on other teams and trades leading up to and at the draft in Buffalo on June 24-25, might be the way Snow goes in remaking a team that finally won a playoff round this spring but still needs to retool to get into the Eastern Conference elite.

Snow historically has made his most drastic maneuvers via trade, starting with his 2007 deadline deal to get Ryan Smyth from the Oilers. He made his biggest splash in October 2014, grabbing defensemen Nick Leddy and Johnny Boychuk within an hour for a combination of prospects and draft picks.

And last June, on the draft floor in Florida, Snow dealt defense prospect Griffin Reinhart to the Oilers for the 16th and 33rd picks. The Isles grabbed Mathew Barzal with that 16th pick, and Barzal might be the best forward addition Snow can make for next season.

But for now — and without knowing who will be offered on the trade market or what Snow is willing to give up — here are a dozen players who might be available for the right price and would upgrade the Islanders in some way for 2016-17 (with contract information from General Fanager and advanced metrics from Hockey Analysis):

James van Riemsdyk, Maple Leafs: He’s only 27 and has two more years left on his contract at a very manageable $4.25-million average annual value. He’s played plenty with Phil Kessel on poor-possession Leaf teams, and when Toronto put a premium on having the puck last season, JVR was among the better possession forwards during a season cut in half by injury.

He very well could be the elite winger Snow finds for John Tavares, and the cost likely would not be prohibitive. Snow and Lou Lamoriello get along well and made the Michael Grabner deal last fall.

Again, a caution: We have no idea who (Brock Nelson? Ryan Strome? Michael Dal Colle?) or what (the first-round pick, 19th overall) Snow is willing to surrender. Sure, the Isles have some contracts they’d love to shed, but you have to give to get to make a deal. We’re just looking at players, mostly forwards, who fit what the Isles are looking for.

Alex Killorn/Ryan Callahan/Nikita Nesterov/Ben Bishop, Lightning: If Tampa Bay manages to get Steven Stamkos back under contract before July 1, Lightning GM Steve Yzerman likely will need to shed a forward or two to not only accommodate his captain’s new deal but those of restricted free agents and must-keep forwards Nikita Kucherov and, after 2016-17, Tyler Johnson and Ondrej Palat. Victor Hedman will need a monster new deal after next season as well.

Killorn fills a few Isles needs: He’s young, he’s versatile (can play center or wing) and he’s played a majority of his minutes the last two seasons with either Stamkos or Johnson, so he’s top line-ready. His playoff clutchness doesn’t hurt either.

Callahan just signed a pretty steep six-year deal with a $5.8- million AAV before the 2014-15 season, with a no-move clause to boot. But the Isles love what he brings and would love to have him bring it in Brooklyn.

Bishop, of course, doesn’t exactly fill a need right now for the Isles, being that they have Thomas Greiss and Jaroslav Halak under contract and J-F Berube as a coveted RFA. But if Bishop is the odd man out with Andrei Vasilevskiy having done a decent job in the conference finals, would the Isles try to ship out Halak and add Bishop as part of a larger deal?

Bishop has a no-move clause but has only one year at $5.95 million AAV left on his deal, and he likely sees the writing on the wall in Tampa. Jack Capuano is a big fan as well.

Nesterov, coming off his entry-level deal, is on here simply because he has a lot to offer as a speedy defenseman, and you can never have too many of those.

Jeff Carter, Kings: L.A. is close to the cap without having signed Milan Lucic. The Kings want to get younger, to be sure, so perhaps Carter could be pried loose.

He’s 31 and his back-diving deal doesn’t expire until after the 2021-22 season, but Carter has been remarkably consistent the past four-plus seasons since he got out of Columbus. He also played a bit with Tavares at the Sochi Olympics, which really means nothing, but there you go.

Valeri Nichushkin, Stars: The 10th overall pick in 2013 hasn’t quite found his stride under Lindy Ruff, and the Stars have a lot of money to shell out to keep their defense corps intact. It seems a very long shot that Dallas would surrender Nichushkin so quickly into his NHL career, but if the Isles were willing, this big wing (6-4, 205 pounds) could be a star alongside Tavares.

Cam Atkinson, Blue Jackets: Columbus has a remarkable level of money already tied up for next season and still needs a deal for Seth Jones, whom they acquired for Ryan Johansen last season.

Atkinson, a Connecticut native, is only 26, is under decent cost control (two more years at $3.5 million AAV) and is a terrific producer for a subpar team. Hard to see the Jackets making this move in the Metropolitan Division, but stranger things have happened.

Beau Bennett, Penguins: Another first-rounder (20th overall, 2010) who hasn’t found his NHL legs yet, even after parts of four seasons in the league. Another one that would be surprising to see within the division, but cost wouldn’t be as prohibitive as some of the other names listed here, and he still could have top-six forward potential.

Wayne Simmonds/Mark Streit, Flyers. Another highly unlikely intra-divisional dream deal, but still. Simmonds would be an ideal wing for Tavares and a quality individual to add to the room.

Ron Hextall has made a lot of forward-thinking moves as Flyers GM, so perhaps the only way Snow could entice his old Philly goaltending partner would be to take Streit’s contract back. The former Islanders captain has one more year at $5.25 million AAV but is standing in the way of a few up-and-coming Flyers defense prospects.

He’d make an expensive 6-7 defenseman, but there’s perhaps no more beloved former Islander out there than Streit.

Jordan Eberle, Oilers. Eberle’s name has been floated an awful lot as the one Edmonton forward who could be moved to help the Oilers upgrade on defense. With Travis Hamonic off the market, an Isles-Oilers swap seems less likely, but perhaps Snow can try dealing another of his defensemen for Eberle, who would come with a hefty price tag (three more years at $6 million AAV) but with another tag: FOJ (friend of John, as he and Tavares go way back).

More Islanders