The Rays’ bullpen has been solid this season, posting a 3.40 ERA that ranks fifth in Major League Baseball. But Tampa Bay apparently is open-minded when it comes to potential upgrades.

The Rays are among the teams keeping in touch with free agent closer Craig Kimbrel, Marc Topkin of the Tampa Bay Times wrote over the weekend.

Kimbrel, a seven-time All-Star, spent the past three seasons with the Boston Red Sox after five seasons with the Atlanta Braves and one season with the San Diego Padres to begin his career. He was expected to land a lucrative contract in free agency, but his market never quite developed, causing him to remain unsigned more than one month into the 2019 campaign.

Kimbrel’s asking price reportedly has dropped — perhaps significantly — since he hit the open market following the Red Sox’s 2018 World Series win. He regressed to some extent last season, though, and his playoff performance left much to be desired. The hard-throwing right-hander also turns 31 later this month, which could further explain teams’ hesitance to offer long-term contracts.

Kimbrel, who rejected the Red Sox’s $17.9 million qualifying offer at the onset of free agency, might benefit from not signing until after the MLB draft, which runs June 3 to 5. At that point, a team no longer would be required to relinquish draft pick compensation in order to sign him, which (finally) could mean a more robust market and a more appealing contract offer for Kimbrel.

Kimbrel posted a 2.74 ERA and recorded 42 saves last season. He has saved at least 31 games in each of the past eight seasons — totaling 42 or more on five separate occasions — while sporting a 1.91 ERA in 542 career appearances.

The Rays entered Monday leading the American League East with a 24-15 record. The New York Yankees (24-16) sat in second place, a half-game back. The Red Sox (22-19) sat in third, three games behind.

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