But they have starkly different opinions on the new format, in which the player who receives the most votes in each conference will serve as a captain, choosing his team from the pool of players voted in as starters and reserves.
"I don't want to do it," Durant told The Athletic. "I'd rather somebody else do it. It's cool to be an All-Star, but all the extra stuff ... I just want to go play in the game. [The new format]'s cool, a different way, a creative way that's good for the fans. But me, I'll let somebody else pick the teams."
Durant (1,326,059 votes) trails Curry (1,369,658 votes) by a margin of fewer than 44,000 votes.
Curry, on the other hand, is on board with the new format of the All-Star Game.
"Why not?" Curry said. "I'll be the first to usher in the new system. I used to go to the playground all the time, and you wanted to be the guy picking teams. That meant you were something on the court back in the day. It'll be a cool vibe to see how it all shakes out and how unique you can make the lineups."
Regardless of who picks the team, Warriors forward Draymond Green wants to make NBA history by sending four players from the same team to back-to-back All-Star Games. Curry, Durant, Green and Klay Thompson made the squad last season.
"I kind of heard quite a bit this year that we should only get three max, but I don't see why not four?" Green told ESPN. "If winning has been the [blueprint to get four stars in] every year, why should it change up?"
As in previous seasons, the starters will be determined by the fan vote, as well as a vote among current players and media. Fans will account for 50 percent of the vote, while all current players and a media panel will account for 25 percent each. Voting will conclude Monday.
Players will be sorted by conference and position (guards and frontcourt players), and the two top guards and three top frontcourt players will be named starters. NBA head coaches will select the reserves. The two captains will then draft a team based on the pool of players.
In the Eastern Conference, Cleveland's LeBron James (1,622,838), Milwaukee's Giannis Antetokounmpo (1,480,954) and Philadelphia's Joel Embiid (784,287) are currently the top three frontcourt players in the fan vote. New York's Kristaps Porzingis (640,928) is fourth. Boston's Kyrie Irving (1,370,643) and Toronto's DeMar DeRozan (537,168) are the top two guards, while Philadelphia's Ben Simmons (397,942) is third.
The starters and captains will be revealed Jan. 18, and the reserves will be announced Jan. 23. Full team rosters will be announced Jan. 25. The All-Star Game will be Feb. 18 in Los Angeles.
ESPN's Ian Begley and Chris Haynes contributed to this report.