Posada, 36, held an impromptu news conference with reporters at Madison Square Garden on Sunday, saying he and the Yankees were "really close" on a new contract as he spoke during halftime of a New York Knicks-Miami Heat game.
After batting a career-high .338 with 20 home runs and 90 RBIs in 144 games for the Yankees this past season, Posada would have been a coveted figure on the free agent market.
He recently said the Mets, Blue Jays and Marlins all had expressed interest. Other notable free agent catchers include Paul Lo Duca, Michael Barrett and Yorvit Torrealba, none of whom came close to matching Posada's production this past season.
Posada's representatives, Sam and Seth Levinson, did not return telephone calls.
The switch-hitting slugger left little doubt about his desire to return to the Bronx.
"My first priority is the Yankees," Posada said Sunday. "I would like to stay with the Yankees. My heart is with the Yankees, so hopefully we can get something done."
The landscape sweetened on Monday afternoon, as the clock ticked down to Posada potentially being available to discuss figures with other clubs. That would have taken effect at 12:01 a.m. ET, with the Yankees then forced to compete with the 29 other teams.
Instead, executive vice president Hank Steinbrenner told the Associated Press the Yankees intended to upgrade their offers to both Posada and free-agent closer Mariano Rivera, both of whom initially were presented with three-year, $40 million proposals, according to reports.
"We're kind of hoping to get an answer at least on one of the two tonight," Steinbrenner told the AP.
"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. We'll see how committed they are."