Benedict's visit to the city was Egan's "golden handshake," papal biographer David Gibson said.
The inspiring trip also was "something of an education for Benedict," Gibson said.
"He got a sense of the kind of qualities needed here."
Egan submitted his resignation as Vatican rules require when he turned 75 last year, but "there was a real sense they were not going to push him out before the Pope's visit," Gibson noted.
With Egan expected to leave his post in the coming months, the two candidates with the most buzz are outsiders - Archbishop Timothy Dolan of Milwaukee and Archbishop Wilton Gregory of Atlanta, the nation's highest-ranking African-American priest, the experts said.
A former New Yorker, Archbishop Henry Mansell of Hartford, is also a possibility. He was the first choice of Egan's predecessor, John Cardinal O'Connor, to replace him.
"A candidate from inside the diocese rarely gets the top job, and Mansell is someone New York priests would like to see in that job," Gibson said. "They don't want somebody from the inside."
Several New Yorkers also are contenders, including Auxiliary Bishops Dennis Sullivan and Gerald Walsh and Bishop Nicholas DiMarzio of Brooklyn.
A spokesman for the diocese did not return messages inquiring about Egan's future.
Church analyst Rocco Palmo, who runs the influential Whispers in the Loggia blog, said he expects Benedict will replace Egan by the end of the year with someone who has proven they can recruit new priests.
"The Pope really underscored the need for new priests," Palmo said. "Archbishop Gregory has really done a good job with recruiting new priests."
Matthew Schmalz, a theology professor at the College of the Holy Cross in Worcester, Mass., agreed that whoever gets the prestigious post will have to do more recruiting and a better job at retaining priests.
Egan was publicly embarrassed when a group of rebellious priests circulated a letter condemning his "arrogant" and "cruel" style in 2006.
Egan defended himself against the criticism during an extraordinary meeting with top aides at the cardinal's Madison Ave. residence.
After the sitdown, his Priest Council - about 30 top aides, including his auxiliary bishops - emerged with a statement strongly defending Egan and blasting his unnamed accusers.
With Benedict's visit now over, Schmalz said, "It might be a good time for Egan to step aside."
"One thing he's been praised for is shoring up the finances of the archdiocese, but he hasn't been praised for dealing with priests," he said.
The Pope "has a reputation for wanting people with administrative excellence," Schmalz said.
Meanwhile, Egan and the rest of the city basked in the afterglow of a papal visit that went off without a hitch.
"We got nothing but kudos for it," a delighted Mayor Bloomberg said. "This city should have a smile on its face. We were very honored to have the pontiff here."
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