The Rays were reportedly in contact with free-agent closer Craig Kimbrel as of late March. A month and a half later, Kimbrel remains without a job, and the Rays are still among clubs “keeping in touch” with the seven-time All-Star, Marc Topkin of the Tampa Bay Times reports.

The 24-14 Rays own baseball’s second-best record thanks in part to their bullpen, which ranks second in the majors in ERA and seventh in K/BB ratio. And they’ve done it without an established closer, having deployed Jose Alvarado, Diego Castillo and Emilio Pagan for at least three saves apiece. All three have been highly effective this season, as has fellow reliever Jalen Beeks, but with the juggernaut Yankees-Red Sox tandem breathing down Tampa Bay’s neck in the American League East, there’s room for outside reinforcements.

The main question for Kimbrel suitors, especially the low-budget Rays, centers on what type of offer would convince him to end his protracted stay on the open market. The 30-year-old entered free agency in November with designs on a contract befitting of a Cooperstown-caliber reliever. However, even after Kimbrel reportedly dropped his price to a more reasonable level last month, the market for the ex-Braves, Padres and Red Sox star has been shockingly tepid.

At this point, with the June 3-5 draft just a few weeks away, Kimbrel seems likely to continue without an employer until sometime next month. As MLBTR’s Jeff Todd explained this week, teams have held off on signing Kimbrel for this long, so it doesn’t seem one will blink until it no longer has to surrender draft pick compensation for adding the qualifying offer recipient.

If the Rays were to sign Kimbrel prior to the draft, though, they’d have to part with their third-highest pick. On paper, that’s the smallest penalty available to clubs, but in the Rays’ case, it would mean losing the valuable 39th overall choice. Of course, the financial ramifications accompanying a Kimbrel signing also seem to stand in the way of a union with Tampa Bay. The Rays own the majors’ lowest 40-man payroll at just north of a paltry $53MM, so there should be room for Kimbrel or another pricey pickup(s) in theory. The franchise has never been known for spending, however, and Kimbrel may land a multiyear deal that would add a sizable commitment to its limited payroll beyond this season.