However, Topkin suggests a deal between the two sides seems unlikely.
This is the first instance of the Rays and Kimbrel being connected, with the frugal Tampa team not known for its free-agent spending. The Rays are projected to enter 2019 with left-hander Jose Alvarado as their closer.
Kimbrel's name has been featured in rumors often lately, with the Washington Nationals and Atlanta Braves linked to the 30-year-old.
The Boston Red Sox, Kimbrel's club for the past three seasons, don't appear interested in a reunion either.
In February, team chairman Tom Werner said the chances of Boston re-signing Kimbrel were "extremely unlikely." Werner's comments came a month after Red Sox president of baseball operations Dave Dombrowski said he didn't anticipate spending significantly on a closer.
Kimbrel has reportedly been seeking a contract worth more than $100 million, and he's also attached to draft-pick compensation after turning down a qualifying offer from the Red Sox following the 2018 campaign.
During his nine MLB seasons, Kimbrel has recorded 333 career saves, a 1.91 ERA, and 868 strikeouts in 532 2/3 innings.
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