As the Royals drift out of postseason contention, they could potentially move Davis for a trade haul similar to what New York received for Chapman. Davis, who will turn 31 in September, is under team control through 2017 on a $10 million club option. He owns a 1.10 ERA and has converted 21 of 23 save opportunities this season.
FanRag Sports' Jon Heyman named the Nationals as one team that has contacted the Royals about Davis, and a source confirmed the report to MLB.com.
Here's a look at the latest from the closer market:
Giants eye Street, Gomez, Jeffress
Closers Huston Street, Jeanmar Gomez and Jeremy Jeffress are reportedly among the Giants' possible trade targets, according to the San Francisco Chronicle. The National League West-leading Giants are in the market for an impact reliever as the Deadline approaches.
Both Philadelphia's Gomez and Milwaukee's Jeffress are in their first season as a closer. Gomez has converted 26 of 29 save opportunities and posted a 2.76 ERA, while Jeffress has 23 saves in 24 chances with a 2.23 ERA.
Street, who will turn 33 next month, has struggled this season and missed time with an oblique strain. His 5.03 ERA is by far the worst his career, and he has just eight saves. The veteran reliever does, however, have familiarity with the NL West, having pitched for both the Rockies and Padres.
Chapman trade fallout
The Yankees' haul for Chapman may have inflated the cost for other clubs to trade for top relief arms.
FOX Sports' Ken Rosenthal speculated that the asking price for Davis or Yankees left-hander Andrew Miller could exceed what the Cubs surrendered to acquire Chapman. Both Davis and Miller are on team-friendly deals that extend beyond 2016, unlike Chapman, who is in line to hit free agency at the end of this season.
Such an increased cost could cool the market, as the D-backs' costly acquisition of Shelby Miller from the Braves did for starting pitchers last winter, Rosenthal said. The going rate for elite relief arms may begin to exceed what teams are willing to offer.
Nats' search for bullpen help not limited to Davis
If Davis can't be had before the Deadline, Washington has several other targets to pursue, according to Heyman, who listed David Robertson of the White Sox and the Cardinals closer Trevor Rosenthal as potential relievers the Nats may seek.
Chicago is said to be open to dealing Robertson, but it's not clear if the Cardinals are willing to trade Rosenthal. The right-hander was ousted as the St. Louis closer late last month, which will likely prompt teams in need of bullpen help, including the Nats, to inquire about his availability.
Jonathan Papelbon is currently manning the ninth inning for Washington. The 35-year-old righty has a 3.62 ERA and 19 saves this season.
Chad Thornburg is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.