Yankees executive vice president Hank Steinbrenner forecast the club's late pushes for both players, telling the Associated Press that Rivera already had received an improved offer and that Posada would be presented with one by the close of business Monday.
Multiple reports indicated the Yankees' original offer for both players had parked in the neighborhood of three years and $40 million, with any tweaks made Monday ensuring a larger windfall.
"The ball's pretty much in their court now. They've both been made very good offers now, and we'll see where they're at," Steinbrenner told The AP. "We'll see how committed they are."
Rivera, who turns 38 on Nov. 29, widely is regarded as the greatest postseason closer in baseball history and a future Hall of Famer. The right-hander owns a franchise record 443 saves in a Major League career that dates back to 1995, with 30 of those saves coming this past season.
Like Posada, Rivera had hoped to negotiate a contract extension in Spring Training but found he was rebuffed, as the team elected to wait until after the season.
After the Yankees' elimination in the American League Division Series, Rivera vowed he would treat negotiations like a "business." Coyly on Monday, Rivera hinted he could even follow manager Joe Torre to Los Angeles if the Yankees' offer was not to his satisfaction.
"The Yankees are my first option," Rivera told The AP in Santo Domingo, Dominican Republic. "But if that is not possible, there is Joe with the Dodgers."
The suggestion of heading west was one that was dismissed on Sunday by Posada, who astutely noted that the Dodgers already have All-Star Russell Martin behind the plate. Los Angeles also has an All-Star closer in Takashi Saito, who recorded 39 saves and a 1.40 ERA in 2007.
Rivera's representative, Fernando Cuza, did not return a telephone message. He is believed to be traveling internationally.
In a telephone interview Monday evening, Yankees general manager Brian Cashman said the team would remain engaged and had not reached conclusions with either player.
"We've made significant efforts to try to keep them, and we surely hope at some point they decide they're going to remain Yankees," Cashman said. "They'll engage the market as well, and they're going to decide for themselves.
"I wouldn't speak for them, but I think it's safe to say they want to come back. We've just got to play it out and give it time. I wouldn't characterize where we're at."