Each ranks among the top 10 in the NL in long balls, and given their power surge through the first half of the year, there's a chance Colorado could be represented at the T-Mobile Home Run Derby on July 11 in San Diego. Eight players in total will be selected.
"I would definitely think about doing it if I was asked," Story said. "You don't get a lot of opportunities to do something like that. But, yeah, I guess we'll see."
Story took the Majors by storm in April when he became the first rookie in MLB history to homer in each of his first four games. The shortstop said he hasn't been contacted to gauge his interest, though Arenado -- who has had an MVP-caliber first half -- told MLB.com that MLB Players Association officials have reached out to him.
Arenado added that he also was contacted last year, told the MLBPA that he would compete in the Derby if selected, but ultimately was not chosen. The reigning Silver Slugger Award winner said this time he has considered the consequences of tinkering with his swing.
"Not the physical toll, the getting you out of your normal swing routine and stuff like that," Arenado said. "I don't know how I feel about that. Obviously, you've seen a lot of good hitters that don't do the Home Run Derby, and that's usually their reasoning is because I don't know about it, my swing, and stuff like that. So, yeah, it is a concern for me.
"But part of me would really love to do it because it's San Diego and I've got a lot of family in California, [and] they would probably try to make the trip to the game."
The format, installed last year, features a five-minute limit for players to attempt to blast as many homers as they can. In the final minute, the clock stops immediately after a home run lands and does not resume until a non-home run ball lands or the batter swings and misses. Hitters are also awarded an additional minute of cuts by hitting any two home runs projected deeper than 420 feet during a single turn, and another 30 seconds if they hit any deeper than 475 feet.
Gonzalez competed under different constraints when leagues each had a captain select their teams and players were granted 10 outs designated to any swing that wasn't a homer. Gonzalez was requested by Matt Kemp in 2012 and didn't make it past the first round, then again in 2013 by David Wright but had to pull out after spraining his right middle finger earlier that week.
"Nolan should be able to do it, but it's up to him," Gonzalez said. "I know that a lot of guys don't want to do it because they're afraid they're going to lose their swing or whatever, but he should do it. I don't think it'll be a problem with him."
Arenado wants to first ensure he's selected to the NL All-Star team before he commits to the Derby, if he's indeed chosen. All-Star voting closes Thursday night, and Arenado was in second place to the Cubs' Kris Bryant in each of the weekly balloting releases made available by MLB.
"It'd be awesome, man," Arenado said. "If Story did it, it'd probably give me more incentive to do it also. But it'd be a lot of fun to have us both there and, like I said, it's an unbelievable honor."
Daniel Kramer is a reporter for MLB.com based in Denver. Follow him on Twitter at @DKramer_. This story was not subject to the approval of Major League Baseball or its clubs.