10:18pm: Heyman reports that Kimbrel’s name has “at least surfaced” in talks with the Yankees, but New York’s reluctance to part with any of Aaron Judge, Luis Severino, Greg Bird and Jorge Mateo would need to change before anything could ever come to fruition. As Heyman notes, the Yankees are checking on nearly all available pitchers, so it’s tough to gauge how much significance to place on the fact that his name has been kicked around.

9:41pm: The Nationals are the team that is “hottest” after Kimbrel, Ken Rosenthal of FOX Sports tweets.

9:43am: The Nationals, Blue Jays and Astros are among the teams to have shown interest in Padres closer Craig Kimbrel, reports Jon Heyman of CBS Sports. The Astros, though, are concerned with the financial commitment that comes along with Kimbrel in the future, he adds.

While many would think the same should hold true of the Blue Jays, it should be pointed out that Toronto can potentially see Mark Buehrle, R.A. Dickey, Dioner Navarro, Marco Estrada and Maicer Izturis depart as free agents this offseason. Additionally, they’ll finally be freed from the burden of the ill-fated Ricky Romero contract this winter. That means more than $50MM will come off their books.

Of course, some of those departures will be offset by a significant increase to Russell Martin’s salary on his backloaded contract ($7MM in 2015, $15MM in 2016) and arbitration raises to players such as Josh Donaldson, Drew Hutchison and Justin Smoak, among others. (Donaldson’s raise, in particular, will be substantial.) Kimbrel’s remaining $3.49MM salary in 2015 would fit into the Blue Jays’ reported $5-8MM in-season spending limitations, though such a move would also limit GM Alex Anthopoulos’ ability to address the rotation, which is reportedly his focus.

The inclusion of the Nationals is a bit peculiar at first glance, given Drew Storen’s excellent 2015 season, but the team has had some bullpen issues beyond Storen. And, as the Royals made abundantly clear in 2014, a deep bullpen is a notable advantage in the postseason. Over the weekend, ESPN’s Jayson Stark speculated this weekend that the Nats could make a play for Kimbrel.

As for the Astros, GM Jeff Luhnow has stated that he’d like to add a flamethrower to his bullpen if an upgrade is made, and Kimbrel’s average fastball velocity is 97.4 mph, so he’d certainly fit that description. His four-year contract’s guaranteed salaries escalate in 2016-17, however. Kimbrel is earning $9MM this year, but that jumps to $11MM in 2016 and $13MM in 2017. He’s also guaranteed at least $1MM via the buyout of his $13MM club option for the 2018 season.

Kimbrel got off to a rough start to his Padres tenure, surrendering 10 earned runs (partially on the strength of three homers) through his first 15 2/3 innings. Since May 19, though, he hasn’t allowed a single homer, and he’s reeled off a 0.76 ERA with a 32-to-10 K/BB ratio in 23 2/3 innings. Recent reports have indicated that the Padres are “pushing” to move some of their big-name, expensive assets.