But Defense Secretary Leon Panetta said Allen had not yet decided about accepting the NATO nomination or retiring from active duty.
Fox News Channel cited a source familiar with the situation as saying Allen, a four-star general who turned over the top command post in Afghanistan last weekend, was essentially asked to retire rather than be re-nominated for the powerful post of NATO supreme allied commander-Europe, which oversees U.S. and allied forces in Europe.
"He's out," Fox quoted the source as saying. "I know he is retiring. He was pushed out of the door."
NBC News first reported Allen was likely to withdraw from consideration from the job -- a nomination put on hold during a Pentagon investigation into emails Allen exchanged with a civilian socialite linked to the scandal that forced Petraeus to resign as CIA director.
Panetta said Wednesday he met with Allen Tuesday and urged him to take time off with his family before deciding whether to accept President Barack Obama's nomination.
Allen, 59, has "been under a tremendous amount of pressure, a lot of challenges," Panetta said at his final news conference before stepping down from the president's Cabinet.
Panetta did not mention the Pentagon inquiry that said Allen -- who is married and has two daughters -- did nothing wrong in exchanging emails with Tampa, Fla., socialite Jill Kelley while he was deputy commander of U.S. Central Command at MacDill Air Force Base in Tampa. Kelley frequently hosted social events for senior officers assigned to the headquarters.
Allen's emails with Kelley came to light during the investigation that ultimately brought down Petraeus, who confessed to an extramarital affair with a separate woman, Paula Broadwell, Petraeus' biographer.
Allen believes despite being cleared of wrongdoing, he does not want to drag his family through a nomination process in which the emails would almost certainly come up, U.S. military officials told NBC.
Panetta said in his news conference he told Allen, "I think your country will always find a way to make use of your great services, but you've got to make the decision as to what you want to do in the future."
An official on Allen's staff said in a statement, "After 19 months in command in Afghanistan, and many before that spent away from home, Gen. Allen has been offered time to rest and reunite with his family before he turns his attention to his next assignment."
Allen also met with Joint Chiefs of Staff Chairman Army Gen. Martin Dempsey this week to discuss the matter, senior defense officials told NBC and CNN.
He was expected to meet with Obama in the coming days, an official told NBC.
Panetta said: "General Allen has been an outstanding commander for the U.S. and [the NATO-led coalition forces]. History, when it looks back, will look at the role played by Allen and see it as pivotal."