What we're failing to recognize here is that a team not "needing" Tavares isn't a reason to pursue him: if he's an upgrade at the 1C position, either by sliding other centers down the depth chart or trading at least one player as a response, then he's worth signing. So the list of teams lining up for him will probably be long. There are many teams that would easily consider a $10m salary.
That being said, there's only a few things he's interested in.
1- A stable ownership and arena situation
2- A team that can be expected to compete for the Stanley Cup over the long haul
3- A crop of young players who are promising and signed long term
4- A good set of linemates for him to play with
5- A reliable front office
6- Teams that could fit him under the salary cap, even if they did what I said above and tried to trade as many pieces as possible
Failing 1 is obviously the largest holdup for Tavares to NYI, and if we're assuming he's in real danger of leaving, then NYI, Arizona, and Florida are not reasonable destinations (Remaining: 28)
Failing 2 is any rebuilding team that won't be good for at least the next three to five years. Teams that fall under this include Colorado, Vancouver, Detroit, New Jersey, and Vegas (Remaining: 23)
Failing 3 is any team on the last legs of their cup window. Teams that fall under this include San Jose and Chicago (Remaining: 21).
Failing 4 is any team with an obviously poor LW/RW group. There aren't that many teams that fail this, but I'd wager Los Angeles does. (Remaining: 20)
Failing 5 is any team with unreliable management. I believe we've already eliminated all the teams that are included in that.
Failing 6 is any team with an obvious cap problem and would be a series of significant moves away to completing this. Toronto, Edmonton, Dallas, Anaheim, Washington, and Ottawa all fail this (Remaining: 14).
Furthermore, there has to be major interest from the team. Which teams would have none, or at best very little? Pittsburgh seems like the only team left who has no need to add another massive money center. (Remaining: 13)
So who is left?
Unlikely - Tampa Bay, Winnipeg, Nashville, Boston, New York Rangers, Columbus (Remaining: 7)
Tampa: Would have to move significant assets to fit Tavares in, along with complicating their long term cap issues.
Winnipeg: Lots of expensive RFAs coming up.
Nashville: Adding Tavares, while possible, would muck up their cap situation significantly for their defensemen.
Boston: 2+ trades including players with NMCs....unlikely but possible
NYR: Although possible, they have a lot of young players that will be coming up looking for raises, and I find it hard to believe Tavares would join the Islanders' biggest rival.
Columbus: They would have to move a bunch of deals, and it may block the payment of Panarin/Werenski
Possible: Buffalo, Philadelphia, Calgary, Montreal, Minnesota (Remaining: 2)
Buffalo: Eichel and O'Reilly are a great 1-2 punch that they probably don't need to allocate additional money, but could if they wanted to move O'Reilly to the wing.
Philadelphia: Any move they make would probably involve shipping out Giroux, but maybe not immediately, since most of their young defensemen won't be coming off their ELCs for a couple years.
Calgary: If Backlund gets less than 6 million and the young defensemen step up, then Tavares could be added. It would likely require a couple of moves, but none are that ridiculous
Montreal: A great situation if Tavares believes the team isn't sinking
Minnesota: A lot of money will be tied up in young players, but there could potentially be enough, especially if they opt not to resign Koivu.
In hot pursuit: Carolina and St. Louis
Carolina: They have oodles of cap space, along with a need for a top-flight offensive presense on a team that desperately needs offense. Especially if Aho, Pesce, Hanafin, and Lindholm can keep from truly breaking the bank, there's plenty of reason to believe a Tavares addition could be in the cards.
St. Louis: With Paul Stastny coming off the books and his 7 million with it, along with their best young players locked up long term, St. Louis is poised to make a major run at Tavares, if he believes in the future of Jake Allen.
My top 5 contenders:
1. Carolina
2. St. Louis
3. Montreal
4. Buffalo
5. Philadelphia