As a result the Yankees will get a compensatory pick in next year's Draft for Robertson, who had declined a qualifying offer worth $15.3 million and was thought to be seeking a pact with a value north of $50 million.
Despite a desire to fill out the rotation, the Yankees have remained out of the bidding for top free-agent starter Jon Lester, who could pick his destination by Tuesday, and have also been quiet on the fronts for Max Scherzer and James Shields.
Cashman and a contingent of Yankees executives arrived in San Diego shortly before 3 p.m. ET and remained sequestered in their suite for conversations with teams and agents. Prior to arrival, Cashman declined to rate his level of optimism for the Winter Meetings.
"Hope doesn't get me anywhere," Cashman said. "You just keep plowing away and just tell people what you're willing to do, and hope that entices them enough."
As for Robertson, he proved himself as a big league closer last season by securing 39 of 44 save opportunities. His agent, Scott Leventhal, had also fielded serious interest from the Astros, in addition to the White Sox and Yankees.
New York added some insurance ahead of Robertson's possible departure by signing left-hander Andrew Miller to a four-year, $36 million deal late last week, and the 29-year-old Miller said that having a strong bullpen is key to the Yankees' chances of getting back to the playoffs.
"Obviously, I'm biased when it comes to the ability of a bullpen to impact games, but I saw the way Boston won the World Series [in 2013]," Miller said. "I thought in Baltimore we had a really, really good group out there, and then obviously, the talk of the town is what the Royals did.
"Despite my biases, I think it's starting to come to the forefront that having good arms to win those games where you're down, or close, is becoming a really valuable part of a team."
The Yankees view Miller and Dellin Betances as a dynamite left-right combo for the late innings, but speaking on Sunday in Stamford, Conn., Cashman said that it was too soon to know how their roles would specifically be set.
"I think it's to be determined [based on] how the rest of the winter shakes out with our bullpen," he said. "If I do some more additions, I think it will declare itself further how [Miller] best fits. I'm not done yet, so we'll see."
With Cashman saying that acquiring starting pitching has proved "easier said than done," the Yankees have expressed interest in retaining members of their own rotation, such as Brandon McCarthy, Hiroki Kuroda and Chris Capuano.
As a contingency, they instructed David Phelps and Adam Warren to prepare for the spring as starters. Their top target in the aforementioned group of free agents is McCarthy, who went 7-5 with a 2.89 ERA in 14 starts last season after beginning the season 3-10 with a 5.01 ERA in 18 outings for the D-backs.
"McCarthy is in the market, he's definitely testing it," Cashman said. "Like every free agent, I think he wants to maximize his value and probably tuck himself in behind the Scherzers and the Lesters and the Shieldses. When those guys sign, I think then he'll really determine what his real market value is."
In terms of position players, New York continues to have interest in third baseman Chase Headley, who has also received overtures from the Giants and Marlins. Because San Francisco is also pursuing Lester, it is possible that Headley will wait for that situation to be resolved before making a decision.
One area in which the Yankees believe they have found an answer is at shortstop, as Didi Gregorius is set to take over the position that Derek Jeter held down for two decades.
Eric Chavez, now a special assignment scout with the organization, was a teammate of Gregorius' with Arizona and gave Cashman's staff a positive endorsement toward acquiring the athletic 24-year-old.
"We talked about him. I was really high on him," Chavez said. "His defense is unbelievable, and hitting-wise he has the potential to be a good hitter -- a good .275, .280 hitter, 12 to 15 home runs. His swing plays perfect for Yankee Stadium; he's kind of got that pull swing. Most of his home runs he hit, where he likes to hit them, I think he'll be pretty successful there."
Chavez said that replacing such an icon as Jeter will present a challenge, but he believes Gregorius will be able to handle the assignment.
"It's tough, but you focus on what you've got to do," Chavez said. "You play hard and you help the team win ballgames, and time will heal that. I think everyone's kind of mourning that loss, but he's an iconic player. Nobody can replace that."