ESPN reported that both the Yankees and the Astros spoke overnight with San Diego about the 27-year-old Kimbrel, who has reached the 30-save plateau in each of the last five seasons.
According to the report, the Yankees would be willing to pick up the approximately $27 million remaining on Kimbrel's contract, but are not budging on dealing their top prospects. It has also been reported that the Yankees have spoken with the Reds about left-hander Aroldis Chapman and with the Marlins about right-hander Carter Capps.
The Yankees' reluctance to deal their top prospects has been a stumbling block. General manager Brian Cashman has repeatedly said that he is hesitant to move players from a group that includes outfielder Aaron Judge, right-hander Luis Severino, first baseman Greg Bird and shortstop Jorge Mateo.
The thinking of adding a late-inning arm is that it would permit the Yankees to further shorten games that have already been impacted by Miller, Betances, Justin Wilson and Chasen Shreve, plus Adam Warren, who has also served as a starter this year and could be returned to the rotation.
In the past week, the Yankees engaged the market for available starting pitchers like Johnny Cueto, Cole Hamels and David Price, but were unable to gain traction in those talks because of the reluctance to deal from the group of their top four prospects.
It is possible that by focusing on the relief market, they will be able to cross the finish line on a deal more realistically.
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch, on Facebook and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.