The Yankees traditionally refuse to negotiate any extensions on existing contracts, but owner Hal Steinbrenner repeatedly has indicated he might make an exception for Cano, who will become a free agent next winter.
Yankees president Randy Levine confirmed Wednesday that the team has talked to Cano's agent, Scott Boras.
"We've had conversations with Scott," Levine told ESPNNewYork.com. "We recognize Robbie is one of the best players in the game, and he is going to be entitled to a significant long-term contract."
Levine's comments came one day after Steinbrenner told a small group of reporters that the Yankees had contacted Boras.
"We expressed to Scott how much we liked Robbie and what a great Yankee he's been, and we hope he continues his career here for a long time to come," Steinbrenner said. "We just indicated to him, on a very preliminary basis, that we were willing to consider a significant long-term contract, and left it at that. There's nothing really to report since then."
Boras confirmed that he and the Yankees had been in conversations for the past three weeks, stating the sides planned to "continue the dialogue."
However, Boras did not indicate whether he and Cano would consider signing an extension with the Yankees without testing free agency next winter.
Cano, 30, will play this season under a team option that will pay him $15 million.
"From a business standpoint, it would make sense for the Yankees to try to sign Cano now," a source told ESPNNewYork.com last week.
The Yankees' willingness to discuss extending an existing deal, a marked departure from their usual policy, indicates not only how badly they would like to retain Cano, but also that Steinbrenner has softened his stance on cutting payroll to $189 million by next season.
"Hal has said over and over again that the $189 million was a goal," Levine told ESPNNewYork.com. "But it must be consistent with the Yankees feeling comfortable that they are fielding a championship team."
Steinbrenner said a year ago that his "goal" was to decrease the payroll to $189 million.
"I'm looking at [a $189 million payroll] as a goal," he said at the time. "But my goals are normally considered a requirement. Plenty of teams win without the kind of payrolls we have."
A source with knowledge of the team's operations told ESPNNewYork.com that until recently, trimming the Yankees' payroll was more than merely a goal.
"It was an absolute mandate," the source said. "And then after the [negative] reaction to it, it became more of a guideline."
The Yankees expect that if Cano, who has averaged 29 homers and 101 RBI over his past four seasons, becomes a free agent, he will receive significant offers from several other teams, including the Los Angeles Dodgers and the Washington Nationals.
Cano's payoff is likely to be in line with the deals recently signed by Albert Pujols ($240 million for 10 years), Joey Votto ($225 million for 10 years) and Felix Hernandez, who recently signed a seven-year, $175 million contract extension with the Seattle Mariners to become the highest-paid pitcher in baseball history.
The Yankees already are committed to paying $86.5 million to five players in 2014, and one of them -- Derek Jeter -- has a player option that could allow him to negotiate a higher salary if he has a good season in 2013. New York avoided signing any multiyear contract this winter other than Ichiro Suzuki's two-year, $13 million deal.
"We can still make a significant offer to Cano and stay within the $189 million limit," Levine said.
Cano batted .313 with 33 home runs, 94 RBIs and a team-high .929 OPS in 2012. The four-time All-Star is a .308 career hitter who is considered one of the best defensive second basemen in the majors.