Rodriguez says on his Web site that he and his wife (Cynthia) spoke "directly with the Steinbrenner family (team owners) ... and we expect to continue this dialogue with the Yankees over the next few days."
Rodriguez said he "reached out" directly to the Yankees. His agent, Scott Boras, did not participate in the talks.
Newsday reported that Hank Steinbrenner, the club's senior vice president, said it appeared Rodriguez "wants to be a Yankee."
It had seemed that Rodriguez was gone after opting out of the final three years of his contract to become a free agent. The Yankees said they would not pursue him.
"After spending time with Cynthia ... and my family over these last few weeks, it became clear to me that I needed to make an attempt to engage the Yankees regarding my future with the organization," Rodriguez said.
He said he and his family "have a foundation with the club that has brought us comfort, stability and happiness."