NASHVILLE – The Toronto Blue Jays are casting a wide net in their search for relievers, checking in on everyone from top free agents to bounce-back candidates.

The Blue Jays have expressed some interest in right-handed relievers Joe Blanton, Yusmeiro Petit and Craig Stammen, according to industry sources.

The Blue Jays don’t comment on specific players, but they’ve made it clear that they intend to upgrade their bullpen. They’re continuing to weigh a wide variety of potential targets in trade talks and free agency. While the Blue Jays have been in touch with Blanton, Petit and Stammen, it’s not clear if they’re priorities or simply options.

“Our priority right now is make the team better and not lose sight of the future,” general manager Ross Atkins said Tuesday at the winter meetings.

Blanton’s best known for his time as a starting pitcher, but he successfully converted to relief in 2015 and has drawn interest from multiple teams, including Toronto. Pitching primarily out of the bullpen for the first time in his career, he posted a 2.04 ERA with more than one strikeout per inning as a reliever — numbers that compare favourably to 2015 free agents like Ryan Madson, Joakim Soria, Mark Lowe and Shawn Kelley. Despite Blanton’s short track record of relief, those numbers intrigue teams.

Petit, who was recently non-tendered by the San Francisco Giants, pitched well out of the bullpen in 2015, posting a 3.67 ERA with 59 strikeouts and 15 walks in 76 innings. In four years with the Giants, the 31-year-old had a 3.66 ERA with 240 strikeouts in 245.2 innings. He has some experience as a starter; he even came within one out of a perfect game in 2013. Petit had been projected to earn $2.4 million in 2016, his final season of arbitration eligibility.

The Blue Jays have also been in touch on Stammen, another recently-non-tendered player who missed most of the 2015 season recovering from surgery on torn flexor tendons in his forearm. He had previously excelled in a setup role for the Washington Nationals, averaging a 2.93 ERA with 74 strikeouts in 81 innings from 2012-14. The Blue Jays are open to including incentives in contracts, an option that could work for players returning from injury like Stammen.

There are dozens of intriguing arms on the free agent market and many more available in trades. Blanton, Petit and Stammen are among them, and there’s no shortage of alternatives for Atkins, assistant GM Tony LaCava and the rest of the front office. Balancing all of the ongoing talks can be equal parts art and science.

“It really is about making sure you’re prioritizing and secondarily having the time to download the conversations physically and also from a strategy standpoint,” Atkins said. “It takes a group and it takes a process.”

While Atkins declined to say how many MLB-calibre relievers he’d like to have at his disposal, some teams attempt to acquire as many as 12. One way or another, the Blue Jays need more relief. They’ve augmented their rotation with Marco Estrada, J.A. Happ and Jesse Chavez, but none of those pitchers has a 200-inning season on his résumé, making the bullpen a priority at the winter meetings.

“That’s important,” manager John Gibbons said. “You can have great starting pitching and they can do their jobs, but if it gets away late every night, that’s never good either. That’s probably more of a focus than anything.”

The Blue Jays have now explored plenty of options on the bullpen front. The next step will be making some of them reality.