"I don't feel this organization is ready to do something like that," Steinbrenner said Tuesday on the Michael Kay Show on ESPN New York 98.7 FM. "No, I do not.
"We'll see. I know that is a number that is out there now. We'll see if he gets it, how much he wants to be in New York. But, again, I can promise it is going to be a very, very solid offer that we do make because we are going to try. We are going to try the best we can to keep him."
The Yankees already feel burned by the 10-year deal third baseman Alex Rodriguez is currently playing on, and Cano will turn 31 years old on Oct. 22. However, he is also a career .309 hitter averaging 28 home runs and 102 RBIs over the past five seasons with the Yankees, including hitting .314 with 27 homers and 107 RBs this season.
Steinbrenner said he is "optimistic" a deal will be reached with the pending free agent, but acknowledged Cano could be wearing a different team's uniform next spring.
"I know that we are going to make him a very, very good offer," Steinbrenner told the show. "Is anybody an absolute must-to-sign? No. And that's nothing against Robby. (It's) just not reasonable to assume that about anybody. We are going to do what we can. We've certainly conveyed to Robby we want him back and we want him to be a career Yankee. We'll just have to see what transpires here."
The Yankees are also awaiting the result of Rodriguez's appeal of a 211-game suspension, which is currently in the arbitration process. If the suspension is upheld and Rodriguez misses the 2014 season, the Yankees stand to save around $31 million off next year's payroll.