Cashman declined to say whether the Yankees' offer was rejected or remained on the table. And he refused to say when the offer was made or if it spurred further discussions.
"I'll just stand with what I said," Cashman said at Steinbrenner Field following the Blue Jays' 1-0 victory against a split squad of Yankees.
Cano did not play Thursday, and he's due to join the Dominican Republic team on Sunday in preparation for this month's World Baseball Classic.
Cashman had hinted that negotiations for Cano could begin this spring. That represents a break from the club's unstated policy of allowing contracts to expire before negotiating - though it's not without recent precedent.
Last spring, the Yankees made a three-year offer to catcher Russell Martin, who played out his option and ultimately signed a two-year, $17 million free agent contract with Pittsburgh.
"Usually that's applied to the older guys," Cashman said of permitting players such as Derek Jeter, Mariano Rivera and Andy Pettitte to reach free agency in recent years before re-signing them. "It's not like it's a country club and here's the code of conduct you can't deviate from.
"We have a history of doing things a certain way, but it doesn't mean you have to do it that way every day."
A significant first strike, and several follow-up offers, might not be enough to keep Cano from hitting the open market. Boras has a history of taking his clients into free agency and pushing for every available dollar.
Whenever he is signed, Cano could wind up in the neighborhood of $250 million.
Prior to last season, Boras got first baseman Prince Fielder signed to a nine-year, $214 million contract with Detroit. Fielder turns 29 in May; Cano turned 30 in October.
Around the league
Rangers • Shortstop Elvis Andrus has been scratched because of what the club called "sensitivity in his left arm" apparently caused by a tattoo. Andrus spent nine hours the two days before Thursday's spring training game against the Indians under a needle. He wanted a likeness of his late father, Emilo Andrus, who died in 1996 when Elvis was 7.
Mariners • Jon Garland pitched for the first time in nearly 20 months as Seattle won its six straight game in a 4-3 win over the San Francisco Giants. Garland, who last pitched for the Los Angeles Dodgers on June 2, 2011, said he was satisfied with his brief outing. He allowed a hit and walked one in one inning.