CLEVELAND -- Craig Kimbrel will reportedly wear a Cubs uniform for the next several seasons, and the Twins could still use bullpen help. So, where does Minnesota go from here?

The Twins were willing to offer Kimbrel a two-year deal, as reported by MLB.com's Jon Paul Morosi, but both the Cubs and the Rays were willing to tack on a third year, according to a report by Ken Rosenthal, with the seven-time All-Star closer reportedly taking the three-year, $43 million offer from Chicago.

No, the Twins didn't ultimately ink the 31-year-old closer and his 333 career saves to anchor the back end of the bullpen, but their pursuit of Kimbrel indicates that team leadership is, as expected, looking to reinforce their relief corps and willing to make additional investments to do so.

Kimbrel would certainly have been an immediate -- and the most historically successful -- boost to this Twins bullpen, which could still certainly use some improving. But also keep in mind that the current 'pen hasn't necessarily been a glaring problem, as the Twins still have the best record in the American League and are 37-2 when leading after seven innings.

In fact, though the Twins have coughed up a pair of late leads within the last two weeks -- against the Brewers and Indians -- the bullpen, as a whole, has still posted strong numbers through that stretch.

"We don't look at a couple of games we've had here and start thinking about things differently," manager Rocco Baldelli said. "We're just going to keep rolling with what we've done. Our guys have come in -- many of them have come in tough spots and succeeded. We're going to continue to roll."

With that said, the Twins had entered the season with the idea that Blake Parker, Taylor Rogers, Trevor Hildenberger and Trevor May would form the core of the back end of their bullpen, but Hildenberger's extended struggles have resulted in a weeks-long demotion to Triple-A Rochester, while May has had issues with his command and has not been a major factor late in close games.

Mike Morin and Ryne Harper have been pleasant surprises as the Twins continue to ease them into higher-leverage roles, while Tyler Duffey and Matt Magill have also been solid. But the depth of the unit as a whole could be a concern, particularly if injuries become a factor.

So, yes, now that Kimbrel is off the table and the Twins have shown an interest in upgrading their bullpen, it figures that Minnesota will turn to the trade market to address their relief needs. The Twins have a robust farm system that could be leveraged in deals, particularly with a deep class of middle infielders set to enter the organization following the 2019 MLB Draft.

Keep in mind: there are still eight weeks remaining until the July 31 non-waiver Trade Deadline, with many quality relievers likely to be available that have already pitched this season. Here's a look at a few of those possible trade candidates:

Will Smith, Giants
Smith would check several boxes. For one, he has back-end, high-leverage experience (27 saves over the last two seasons). He has showcased strong command this season (four walks in 22 2/3 innings), which has been an issue at times for the Twins' relief corps. The Twins also only have one left-hander in their current bullpen (Rogers), and another southpaw would be a big addition to a potential playoff roster.

Shane Greene, Tigers
The 30-year-old right-hander has bounced back from a tough 2018 to lead the American League with 19 saves, with 28 strikeouts and only seven walks this season. He has an additional year of team control beyond 2019.

Ken Giles, Blue Jays
Part of Giles' appeal is that he has the overpowering fastball (averaging 97.2 mph this season) that the Twins' current high-leverage options don't possess, and that he also has experience pitching in the postseason -- though he struggled for the duration of the Astros' run to the World Series in 2017.

Alex Colomé, White Sox
Colome has plenty of back-end experience (108 career saves), and though his fastball velocity is down a tick or two this season, the cutter he's throwing for most of his pitches has generated both a ton of whiffs and plenty of weak contact. He also has a year of team control remaining.