Robinson Cano of the Yankees celebrates his third-inning, three-run home...

Robinson Cano of the Yankees celebrates his third-inning, three-run home run against the Kansas City Royals with teammate Alberto Gonzalez at Yankee Stadium. (July 10, 2013) Credit: Jim McIsaac

HOUSTON -- Like everyone else, Robinson Cano has been swept up by this season's emotional farewell to Mariano Rivera and the recent goodbyes to another member of the Yankees' Core Four, Andy Pettitte.

But Cano said Friday he's not about to sell himself short merely for the chance at a similar pinstriped legacy. Even with a front seat to history this past week, the second baseman has never taken his eye off the ball.

Or in Cano's case, the goal of a record-setting 10-year, $310-million contract, as sources said he asked the Yankees for earlier this season.

"Don't get me wrong -- I love this organization,'' Cano told Newsday before Friday night's series opener at Minute Maid Park. "But I know at the same time, they're going to do what they think is best for them and I'm going to do what I think is best for my family.''

Cano did not say those two things are mutually exclusive, and in no way did he dismiss the possibility of signing an extension with the Yankees. But the two sides are miles apart when it comes to evaluating the player's worth -- which is why the Yankees and Cano's camp cut off negotiations weeks ago.

"I haven't said anything about 'I'm leaving' or 'I'm staying,' '' Cano said. "That time is going to come. I just want to take the next month or two months, whatever it is, and sit down with my family. Discuss everything and see what we want to do.''

As far back as spring training, the Yankees seemed confident that they would lock up Cano long before he ever got this close to free agency. But the tenor of the relationship changed when Cano dumped Scott Boras to become the first superstar client of Jay Z's new agency, Roc Nation Sports.

At that time, Boras and the Yankees believed they had made progress toward keeping Cano in the Bronx. Any offers since the Boras separation, however, have been summarily rejected, according to sources. The first was an eight-year, $138-million contract modeled on the one David Wright received from the Mets last November, followed by a six-year deal in the $145-million range that pushed the average annual value to roughly $24 million, sources said.

During the course of those negotiations, the Yankees had a sense that the talks eventually would get to the same level as the eight-year, $180-million contract they gave to Mark Teixeira in 2009, according to a source. But the club was stunned, sources said, when Cano's reps countered with a 10-year deal that could be worth as much as $310 million, a whopping figure that signaled to the Yankees that he is headed for free agency.

When Cano was asked Friday if he indeed requested $310 million from the Yankees, he smiled and said, "I don't want to go into details. Sometimes it's better if you don't say anything.''

Throughout this season, Cano has remained silent on the contract front, preferring to keep the focus on the field. And despite little protection in the lineup, he entered the final weekend batting .313 with 27 home runs, 106 RBIs and an .899 OPS. Entering Friday night, in the last 48 games, Cano was hitting .369 with six homers, 36 RBIs and a .988 OPS.

Cano shrugged when asked if he is disappointed that an extension didn't get done during the season, saying, "It could have happened either way.'' But there was some satisfaction that he helped keep the attention on Rivera during his farewell tour.

"The biggest thing is that I've got a lot of time,'' Cano said. "This was Mo's year -- a guy that I loved to death, a guy that I appreciate for everything, a guy that was there for me, a guy that always gave me good advice. I just wanted to forget about the business part. I didn't want to talk about a contract. I just want to enjoy and have fun the next few days.''

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