However, it's no guarantee, Mozeliak cautioned, that they even find an upgrade there.
"I don't feel like we have to do something," Mozeliak said shortly before first pitch Sunday. "I do feel there have been past years where it's been very clear what we needed to do. And this year I feel it's a little blurry. But there's still a week left in this. We'll see where we feel comfortable possibly doing something."
The Cardinals' bullpen seems to be emerging from its recent funk, which coincided with a shift in roles. Seung Hwan Oh has assumed the closer's job, and Kevin Siegrist's return from a bout with mononucleosis has given the Cardinals a second setup option along with Jonathan Broxton.
The organization's confidence that Trevor Rosenthal and Seth Maness can regroup from troublesome season starts to provide meaningful innings also lessens the desperation of finding help elsewhere.
"I do feel like this team as a whole, there has been a more positive vibe since the All-Star break, and even prior to the All-Star break we went in with some bounce in our step," Mozeliak said. "Just building on that and trying to manage it."
The fact that the trade market appears fruitful in relievers, though, should help the Cardinals increase their chances of finding an external fit. In recent years, the club made somewhat low-profile bullpen adds midseason -- Marc Rzepczynski and Octavio Dotel in 2011, Edward Mujica in 2012, Broxton in 2015 -- that ended up being impactful.
Aside from a potential bullpen addition, don't look for the Cardinals to be all that active over the next week. They intend to fill some holes on the field by getting healthy, and their thin catching depth isn't so much a concern given Carson Kelly's development in the Minors this season.
Jenifer Langosch has covered the Cardinals for MLB.com since 2012, and previously covered the Pirates from 2007-11. Read her blog, follow her on Twitter, like her Facebook page and listen to her podcast. This story was not subject to the approval of Major League Baseball or its clubs.