The red-headed stepchild of the Winter Classic, the Stadium Series allows the NHL to stage an outdoor game between two unlikely opponents - like sunbelt teams or Canadian teams or teams that have played in the Winter Classic too recently to play in it again already. As the Winter Classic (and its Canadian counterpart the Heritage Classic) virtually prints money for the league, it is no surprise the NHL has expanded its slate of outdoor games.
The status of a Sharks-hosted game likely hinges on the success of the outdoor game held in Dodger Stadium between the Los Angeles Kings and Anaheim Ducks. The climate in Chavez Ravine should be fairly similar to whichever venue the Sharks host their game, so the NHL could see if the ice surface can withstand the brutal Californian winter.
The NHL is likely also seeing if an outdoor hockey game can draw in the somewhat nontraditional Golden State market. By hosting a Stadium Series game between the only two Western Conference teams that share a media market, the NHL gives the game a bit of a safety net, being able to easily draw from the two fanbases, casual and die-hard alike. A game hosted by the Sharks does not have a similar double-dip draw. If the Dodger Stadium game is a resounding success, the NHL would feel more comfortable removing the second team safety net.
Kurz lists AT&T Park as the obvious first choice - it's an iconic park with a backdrop made for TV. It would be a draw for imagery alone. However, there's the question of San Francisco's unique climate; the humidity may affect the ice to a point where it's even worse than the Pittsburgh-Washington Winter Classic.
On the other hand, I could see Levi's Stadium as the venue of choice. It is much closer to San Jose than China Basin, has a higher capacity, and has the bonus of being in its inaugural season when this hypothetical outdoor game is played. While there may not be the same dramatic backdrops as at AT&T Park - though I would enjoy the occasional shot of
Top Gun Flight Deck during the game - the ice would probably be better. There are scheduling issues that exist with Levi's Stadium that aren't a problem at AT&T, what with the 49ers playing during the winter.
The potential opponent is even more of a mystery. All three of the biggest division rivals (LA, Anaheim, and Vancouver) are playing Stadium Series games in this upcoming season. Though the NHL has not shied away from having the same teams play outdoor games, that honor has yet to be bestowed upon a team outside of the eastern time zone. Dallas is the next obvious choice, but it seems they are destined to play Minnesota. My guess would be Vancouver, despite the repetition, because of the recent playoff rivalry and the fanbase's willingness to travel/pay outrageous ticket prices.
All that being said, the Sharks are still only in the running to host an outdoor game, and this is no sure thing. It could be that every team in the league is in the running for hosting a Stadium Series game next season. But it's still kind of awesome to think about, isn't it?