ESPN Deportes quoted a source as saying the Mariners would be willing to go up to 10 years and $240 million for Cano, who reportedly has been offered seven years at about $170 million by the Yankees.
FOXSports.com reported that Cano asked for $240 million but that the Mariners have not offered more than $200 million.
On Wednesday, Mariners general manager Jack Zduriencik was keeping quiet.
The Yankees, meanwhile, are still talking with Cano.
"We're still talking," Yankees managing general partner Hal Steinbrenner said Thursday at Yankee Stadium, where the club was introducing new catcher Brian McCann. "Nobody has given up. We're still talking, but obviously, we're a decent distance apart. We're just going to have to see, day by day. That's all we can do."
More than rumors happened Thursday, as numerous deals went down:
• The Royals acquired outfielder Norichika Aoki from the Brewers for left-hander Will Smith. Here's the Royals' side, the Brewers' angle and MLB.com's Phil Rogers writing that the trade is a win-win for these clubs.
• The Red Sox signed right-handed reliever Edward Mujica for two years and $9.5 million.
• The Dodgers re-signed reliever Brian Wilson to a one-year, $10 million deal.
• The Marlins have agreed to a one-year deal, pending a physical, with Rafael Furcal, who will play second base.
• The Rangers inked a trio of Minor League free agents, including righty Jose Contreras, who turns 43 on Friday.
• The Cubs signed left-handed reliever Wesley Wright to a reported one-year, $1,425,000 deal that also has him under team control in 2015.
• The White Sox and right-handed reliever Ronald Belisario agreed to a one-year deal.
In other news, Major League Baseball and Nippon Professional Baseball continue to close in on a deal that would revise the current posting system.
Other notes from around the big leagues:
• The Yankees officially introduced McCann.
• Yankees general manager Brian Cashman said free-agent right-hander Hiroki Kuroda "wants to come back" for a third season in the Bronx.
• The Rays re-signed right-handed reliever Juan Carlos Oviedo to a one-year deal.
• Toronto is looking to upgrade its rotation but is content with its production at second base.
• Orioles reporter Brittany Ghiroli answers reader questions in this inbox, including one asking who will take over the closer's role for the recently traded Jim Johnson.
• The Twins officially introduced right-hander Phil Hughes.
• Infielder Willie Bloomquist is excited for his return to Seattle.
• Astros manager Bo Porter is pleased with the club's acquisition of outfielder Dexter Fowler.
• Braves right-hander Brandon Beachy is confident he'll be at full strength by the time Spring Training starts, after missing much of the past two seasons rehabbing from Tommy John surgery.
• The Phillies signed Wil Nieves to serve as backup catcher and right-hander Jeff Manship to a Minor League contract with an invitation to Spring Training.
• The Marlins likely won't deal from their young pitching depth.
• Among other things, Mets reporter Anthony DiComo breaks down the pros and cons of the club pursuing free-agent outfielder Curtis Granderson in this inbox.
• Cubs manager Rick Renteria finally made it to Wrigley Field on Thursday to be formally introduced.
• The Cubs plan on keeping top prospect Javier Baez at shortstop at this stage in his development, as reporter Carrie Muskat writes.
• Cardinals reporter Jenifer Langosch fields fan questions in this inbox, including her thoughts on when prospect Oscar Taveras will be ready for the bigs.
• Right-hander Daniel Hudson is optimistic he'll return to the D-backs.
• With Fowler in Houston, Carlos Gonzalez is a candidate to lead off for the Rockies.