ST. LOUIS -- As soon as Trevor Rosenthal walked off the Fenway Park mound, his elbow aching after an abbreviated August appearance, the Cardinals found themselves thrust into a market that they hadn't necessarily anticipated wading into this winter.

To rebuild the bullpen, they're having to start from the back.

It's been 16 years since the Cardinals last entered an offseason needing to add a closer from outside the organization. Jason Isringhausen was the answer in 2001, and the Cardinals will cast a wide net while searching for their next ninth-inning fit.

They have the option of pursuing established closers or those who they feel can evolve into a future one. General manager Michael Girsch, speaking at the GM Meetings in Orlando this week, hinted at the Cardinals' Plan A.

"I think our preference," he said, "would be someone who has closing experience."

"Preferable," president of baseball operations John Mozeliak added, when asked about the same topic. "But it doesn't necessarily mean it has to happen. I think over the next couple weeks we'll have a much better sense of where that market is going and names and faces that might really be [true] fits."

Relievers with closing experience are limited on this year's free-agent market. There are four players who saved more than 20 games in 2017, with Wade Davis and Greg Holland considered to be at the head of the class. There's also Brandon Kintzler, who tallied 29 saves for the Twins before being dealt at the non-waiver Trade Deadline.

Hefty price tags will be attached to all three. Consider that last year's top trio of free-agent closers signed deals for $86 million (Albertin Chapman), $80 million (Kenley Jansen) and $62 million (Mark Melancon). For a team that is also seeking to upgrade its offense and rotation, the Cardinals will have to determine whether such a cost is palatable or prohibitive.

If it's the latter, the club can pivot to the trade market or perhaps pursue a setup man who it feels is ready for the role change. MLB.com's Jon Paul Morosi reported on Wednesday that the Cardinals have engaged the Rays in discussions about Tampa Bay closer Alex Colome, who led the Majors with 47 saves last season.

Colome does become arbitration eligible this offseason, so his salary is set to see a substantial spike. But he also has three years of club control remaining, something that would be appealing to the Cardinals. 

Regardless of the direction the Cardinals choose, their bullpen makeover isn't likely to begin and end with one move. Girsch noted that "adding multiple relievers is one thing we're trying to accomplish." Driving that preference is the fact that the Cardinals have already removed four relievers -- Zach Duke, Seunghwan Oh, Juan Nicasio and Rosenthal -- from their 40-man roster since the end of the season.

But filling multiple holes will require some creativity. The Cardinals are considering pitchers who could serve as swingmen between the bullpen and rotation, depending on need. They'll also explore low-risk relievers in whom they see potential.

"Some of them might not be glamorous," Girsch said. "Our goal is to add depth to our bullpen every way we possibly can. Some of them might not be relievers people even notice when we sign them, but hopefully we're adding depth. You can have impact signings that end up being impact signings that aren't perceived as such."

Girsch cited Brandon Morrow as a recent example of this sort of find. Morrow signed a Minor League contract in late January, spent two months in Triple-A and then finished the year as the setup man for the pennant-winning Dodgers. He had a modest salary of $1.25 million.

The Cardinals had similar success in 2014 when they brought in Pat Neshek in on a Minor League deal. Neshek wound up having an All-Star season.