Rivera received a three-year, $45 million contract offer from the Yankees before he was eligible to discuss financial terms with other clubs, a proposal he has not accepted.
Rivera's agent, Fern Cuza, has not responded to telephone calls requesting comment. The New York Times reported Friday that Yankees general manager Brian Cashman spoke with Cuza on Thursday but that the Yankees have no plans to improve the offer further.
"They haven't rejected it outright, as far as I know," senior vice president Hank Steinbrenner told the Times. "It's pretty much known that they're seeking a fourth year, or more [money] for three years.
"I want him back, and that's why the offer is as high as it is. We don't have to change anything. Everyone in baseball knows it's a great offer; we've even gotten a couple of complaints about it."
Rivera's interest in a fourth year may have been piqued when another lifelong Yankee, catcher Jorge Posada, agreed to a four-year, $52.4 million deal earlier in the week, bypassing the chance to negotiate with other clubs as a non-restricted free agent.
Both Posada and Rivera had expressed interest in negotiating contract extensions during Spring Training, but were rebuffed by the team. After the season, Rivera -- who was 3-4 with a 3.15 ERA and 30 saves in 67 games -- vowed that he would treat negotiations like a "business" and that all 30 teams would have an equal chance to procure his services.
Rivera holds an American League record with 443 saves and has a Major League-record 34 saves in the postseason, accomplishments which almost certainly will open the doors to Cooperstown five years after his retirement.
Rivera has achieved all of his numbers in a Yankees uniform, but speaking in the Dominican Republic this week, he floated the idea that he could leave New York and pitch for Joe Torre with the Dodgers if the contract terms with the Yankees were not to his satisfaction. Yet the Dodgers appear set at the closer position with All-Star Takashi Saito.
Speaking in New York this week, Torre told the Associated Press that he expects Rivera to stay with the Yankees.
"I haven't talked to him about it, but I'd be surprised if he didn't," Torre said. "He's state-of-the-art for me. I don't know what he's thinking at this point in time."
New Yankees manager Joe Girardi, visiting the Dominican Republic on a scouting trip, told the AP that he met with Rivera on Wednesday. He also has a strong feeling that when he fills out his first lineup card for the Yankees, Rivera will be available in the bullpen.
"I think that there is a good chance that he will return to the team," Girardi said Thursday.
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.