"He has a significant contract as it is," Cashman told the Web site SI.com. "So I don't anticipate any dialogue regarding an extension."
Rodriguez would have three years and $81 million remaining on his $252 million contract after this season, but he holds a contractual opt-out clause that could make him a free agent after the year.
The Yankees would owe $50.7 million for the final three years of Rodriguez's contract, with the Texas Rangers assuming the remainder, including deferred payments.
Rodriguez told reporters Thursday that he was "not surprised" by Cashman's comments and that nothing has changed in his situation.
"It can come up every day of the year, I'm going to give you the same answers," Rodriguez said. "You guys ask the questions, I'm going to answer you the same way. It's really not a big deal."
Cashman's statement regarding Rodriguez is consistent with the Yankees' inclination not to negotiate extensions in-season during 2007.
Closer Mariano Rivera and catcher Jorge Posada are among the team's players in contractual walk years, in addition to manager Joe Torre. Cashman has stated that the club is not prepared to engage in any such discussions.
Rodriguez said in a recent radio interview that he wants to remain in New York for the remainder of his career, but said that he wants to make sure he has the support of Yankees fans and management.
"One-hundred percent, I want to stay in New York City," Rodriguez said March 14. "Period, that's it. I don't know how many more ways I can say that."
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.