The first report regarding the Braves and Andrelton Simmons came out last night, when Jonah Keri, formerly of Grantland, reported that the Braves were "deep" in trade talks with an NL West club, without elaborating further.
Keri then reported that the Braves were discussing Simmons with the NL West club, again not mentioning which team was involved in the discussions. The Giants, by this time, had been ruled out from being the team in the discussions.
The Padres, Dodgers, and Angels
According to Joel Sherman of the New York Post, the Padres, Dodgers, and Angels all engaged with the Braves about Simmons.
The Padres and Angels have a direct need for a shortstop.
San Diego resorted to using Will Middlebrooks and Jedd Gyorko, both non-shorstops, to play the position at some point during the year. However, they likely do not have enough prospect power to be able to pry Simmons away from the Braves. The team depleted its farm system last offseason, when they traded for the likes of Middlebrooks, Justin Upton, and Derek Norris. Outfielder Hunter Renfroe is the Padres' top prospect, according to MLB Pipeline, but even he probably would not be enough to get a deal done.
As for the Angels, they are probably more likely to get a shortstop via free agency than through trade, but the middle infield is an obvious need for them.
The Dodgers don't make direct sense for Simmons, as top prospect Corey Seager plays shortstop and impressed during his first cup of coffee in the Major Leagues. However, some have speculated that they could slide Seager to third, where has some minor league experience, and play Simmons at short. But for the time being, they probably are not a likely destination for Simmons if he does get moved.
The Mets also have coveted a shortstop for quite some time now, and according to Jon Heyman of CBS Sports, they are in contact with the Braves regarding Simmons. However, Sherman reports that Atlanta is asking for either Matt Harvey or Jacob deGrom in the talks.
Obviously, the Mets don't want to deal two of their top starters. This also isn't a good indication of the Braves asking price, as they'd probably ask for more in return from an inner-division rival. But, it does show how much the Braves value Simmons and how they want an impact return to move him.
According to multiple reports, in reality, the Braves are just listening on Simmons, who is under team control through 2020. They'd need a great and organizational-changing return for Simmons to actually be traded.