The "Core Four" is down to two.
The source told Olney that Posada, 40, is trying to determine the right time to make an announcement, which is expected to be in the next two weeks.
Pettitte retired after the 2010 season.
Only Bill Dickey and Yogi Berra have caught more games in pinstripes than Posada (1,574).
But Posada lost his catching job before the start of last season and struggled early in his new role as the designated hitter. The switch-hitter was batting .165 against left-handers on May 14 when he was dropped to No. 9 in the batting order and asked out of the game against Boston.
Posada hit .235 with 14 home runs and 44 RBIs last season.
He then hit .429 in the five-game division playoffs series loss against Detroit, receiving several long ovations and chants of "Jor-ge! Jor-ge!" at Yankee Stadium.
After Posada's final game last October, he was asked what playing for the Yankees had meant to him -- and he broke down in tears, before walking away from reporters.
Posada probably could have continued his career somewhere as a designated hitter and padded his career numbers of 275 home runs, 1,065 RBIs and 936 walks. But Posada always cherished the privilege and responsibility of being the Yankees catcher.
He viewed Thurman Munson as an idol, and converted from second base to catcher after being drafted by the Yankees in the 24th round of the 1990 draft.
Swinging with pine tar on his hands, and without batting gloves, he was a five-time All-Star, caught David Wells' perfect game in 1998, and played in 125 games in October. He is a borderline Hall of Fame candidate, but his legacy as a Yankee probably means more to him.
ESPN The Magazine's Buster Olney contributed to this report. Information from The Associated Press was used in this report.