So as he was asked about it again and again and again during his All-Star media availability, Stanton was completely unfazed.
"Pretty simple," said Stanton. "Just don't read rumors. Anything important is going to come from your inside circle and you'll know when it's legit."
To this point in his career, nothing has been "legit" enough for Stanton to have to pack his bags and leave Miami.
Yet the 24-year-old Stanton has two more years of arbitration-eligibility left, which leaves an open-ended amount of rumors to come as long as he wears that Marlins uniform.
"That's with a lot of other players, also," Stanton said. "When you're in the arbitration system and don't have a deal or whatever, there's going to be those kind of talks, always, whether you just start or you're a few years down the road. There's nothing I can do about it at the moment. I'm just going to go out and play and worry about things like that when it comes."
Meanwhile, National League pitchers will continue to worry about Stanton's imposing presence in the batter's box. This season, he has 21 homers in 353 at-bats.
"You've got a guy who can hit 700 feet in the batter's box, you kind of feel uncomfortable," said Braves closer Craig Kimbrel.
And even if Stanton has yet to taste playing in a pennant race, he is comfortable being a Marlin until someone tells him he's not anymore.
"You never know, man. You never know what's going to happen," said Stanton. "I'm here now and we're battling and trying to get this spot in the playoffs. I'm not worried about where I am two, three years from now. You don't worry about that stuff."
Of course, fans of teams that could use a big bat like Stanton's will continue to obsess about what it would be like to watch him play every day.
"People do think about it, but I can't," Stanton said. "If I'm thinking about every rumor or everything something said about me, I'd be all over the place. You filter what you need to and you stay on course."
At least on Monday, that course was in the middle of the All-Star spectacle, where Stanton was set to participate in the Gillette Home Run Derby. For Tuesday's game, he was selected by National League manager Mike Matheny to be the designated hitter.
"He's a pretty impressive guy," Matheny said of Stanton. "I think anybody who has had to deal with him and watch the impact he has on the game, an impact he has on the lineup, you have to give a great deal of respect not just on the power ... but the ability he has to turn around the game on one pitch. I'm not sure I've seen a guy since [Mark] McGwire that hits the ball as hard as Stanton does."
Stanton will bat fifth for the NL.
"We're going to help the team and help try to get that home-field advantage, and I'm glad I can start and do that," said Stanton.
And Stanton didn't represent the Marlins by himself. Right-hander Henderson Alvarez was recently added to the roster as an injury replacement.
"Well-deserved also," Stanton said of Alvarez. "It will be good for him, and his family is here and everything, and he'll get to soak up the whole environment and situation, so I'm happy for him."
Like the rest of the Marlins, Alvarez enjoys the possibilities every time Stanton steps to the plate.
"Stanton is a complete player," Alvarez said. "He's the head of our team. He's the No. 1 guy on our team and I'm overjoyed to be out here with him and to share this experience with him."