"When we made the qualifying offers, we did not expect anyone to accept," Cashman said. "We would have been happy if any of them did. So, now we enter the remaining part of the process, stay engaged and try to re-sign our players."
If any of the three players sign with other teams, the Yankees will receive a compensation-round pick in next year's First-Year Player Draft.
Cashman said that he spoke to some agents on Monday as the GM Meetings got underway at the JW Marriott Grande Lakes, and setting the bedrock for trade talks with other general managers is often a big part of these proceedings.
Cano's representative, Brodie Van Wagenen, is on the ground at the GM Meetings, but Cashman said that any progress toward an agreement with Cano -- who reportedly asked the Yankees for a 10-year, $305 million contract -- will take time.
"He has earned the right to be a free agent and he's a premier player," Cashman said. "Given that status that he carries, those types of players dictate the dance steps. We'll do the dance as long as we can, but at some point you can't do that forever. We're in the very front end of this thing. The music hasn't even started yet."
There had been speculation that Granderson might accept the one-year contract in order to improve his statistics coming off an injury-shortened season, but Granderson's power bat should give him choices to pursue a multiyear contract as a free agent.
Granderson is said to have interest in returning to the Yankees, who have several outfielders already on the roster with Alfonso Soriano, Brett Gardner, Ichiro Suzuki and Vernon Wells. Presented with those names, Cashman seemed to indicate that the Yankees are not satisfied with the idea of standing pat.
"I think I'm actively looking to improve all aspects of the club," Cashman said. "Do we have outfielders that we're ready to start the season with? Yes. If I can improve upon that, all the better. Same with the infield.
"I have question marks with the [Alex Rodriguez] controversy at third, I have a question mark at short with Derek Jeter coming back from his ankle, a free agent in Cano. Ultimately, I need to look and be open-minded to improving all aspects when I can."
The qualifying offer arguably seemed to fit Kuroda best, given his stated preference for operating on one-year contracts and his $15 million salary last season. But Cashman said that Kuroda has not yet expressed what he hopes to do in 2014, whether it be to pitch for the Yankees, another Major League club or perhaps to return to Japan.
"The only information I've gotten about that [is] that he hasn't made any decisions what he wants to do as far as next year is concerned," Cashman said. "He's really good at what he does, he's a pro in that clubhouse and off the field, so he's going to have a lot of choices."
Asked if Kuroda seemed to be contemplating not pitching in 2014, Cashman said that the tone of his discussions with agent Steve Hilliard have been more similar to last season. That's good news for the Yankees, who need to keep as many options open as possible.
"The bottom line is, I'm glad Opening Day is not tomorrow, because we have some work to do," Cashman said.