Officials said Kerry has asked his staff to further develop the idea and raised the issue at a National Security Council meeting last week, where Obama discussed the U.S. strategy for stemming the bloody civil war in Syria with his top advisers.
Kerry "wants to revisit this and for it to be looked at more seriously," one senior administration official said, adding that the secretary of state has been advocating within the administration for "more robust measures" in Syria.
While the primary discussion at Thursday's NSC meeting was about the northern border with Turkey, the officials said there has been some initial talk about an additional no-fly zone near Syria's southern border with Jordan, although another official said the southern option "was even less thought out."
"I expect this discussion process to go on quite intensively for the next few weeks," the second official said.
Officials said a no-fly zone was one of many options being discussed among the President's national security advisers and with U.S. coalition allies on the sidelines of the U.N. General Assembly last week in New York.
While the idea was not rejected out of hand by the White House, administration officials emphasized that such a safe zone is not currently being seriously considered.
"What the secretary has been doing is looking for ways to increase pressure on ISIL, ease the humanitarian burden, and increase leverage for diplomacy to end the conflict," a third senior administration official said. "In that context, this is one of many ideas that he and others discussed."
The official was using another acronym for ISIS, which the U.S. is trying to eradicate from Syria and neighboring Iraq.
In the interim, Obama did authorize the resupply of Syrian Kurds and Arab-Syrian opposition as part of the strategy to put pressure on ISIS from the north and strengthen the border, according to two senior administration officials. The approval came at the Thursday NSC meeting.
Kerry's predecessor, Democratic presidential candidate Hillary Clinton, along with some 2016 Republican candidates have backed the idea of a no-fly zone. But the President dismissed the idea when asked at a press conference Friday whether he would consider a no-fly zone like Clinton is proposing.
"When I hear people offering up half-baked ideas as if they are solutions, or trying to downplay the challenges involved in this situation -- what I'd like to see people ask is, specifically, precisely, what exactly would you do, and how would you fund it, and how would you sustain it," Obama said. "And typically, what you get is a bunch of mumbo jumbo."
The President then clarified that as commander in chief, his discussions with U.S. military advisers gave him a fuller picture of the pitfalls of such a strategy than presidential candidates on the campaign trail.
"We all want to try to relieve the suffering in Syria, but my job is to make sure that whatever we do we are doing in a way that serves the national security interests of the American people, that (it) doesn't lead to us getting into things that we can't get out of or that we cannot do effectively," Obama told reporters.
The press conference came just one day after Kerry raised the idea in the NSC meeting.
Turkey, France and the Syrian opposition have long pushed for a safe zone to protect civilians from Syrian airstrikes, but the Obama administration has repeatedly rejected the idea as too difficult to implement.
Senior administration officials said serious logistical concerns remain, including who would enforce it and the need to divert resources from the campaign against ISIS. The U.S. military has not supported a no-fly zone, in part because of the myriad actors in the skies over Syria and the difficulties of vetting the people who would be allowed inside.
Although Kerry revisited the idea of a no-fly zone primarily to put pressure on ISIS and protect civilians against Syrian regime attacks, officials said the idea has a new context with Russia's military intervention in the war-torn country.
Senior administration officials said Russian airstrikes have repeatedly targeted CIA-backed rebels, despite Moscow's assertion that it is only attacking ISIS targets.
"It seems Russia is basically carrying out airstrikes where the rTegime is under threat and is deliberately targeting groups fighting against (the) regime," a senior Western diplomat said. "The idea that they are going after ISIS is pretty paper thin."
Additionally, Russian planes have twice crossed into Turkish territory, violating the airspace of a NATO ally.
One official said a no-fly zone could have the added benefit of complicating Moscow's action in Syria.
"One hopes this would be a good secondary effect of putting pressure on Russia," one official said.
But Russia's air campaign only further complicates any effort to impose a no-fly zone, raising the risk of U.S. and Russian military jets facing off in the skies. The U.S. and its allies desperately want to avoid getting into a military confrontation with Russia.
"There (were) a lot of discussions last week about how to respond to the Russians and a no-fly zone has been discussed as an option to call their bluff, stop the barrel bombing and protect civilians," the Western diplomat said. "But I'm not sure that's where the debate is going. None of this would get any easier with Russia planting themselves in Syria."
Although Obama doesn't currently support a no-fly zone, his position on U.S. involvement in the conflict has evolved.
During his first term, Obama vetoed proposals by then-Defense Secretary Leon Panetta and Chairman of the Joint Chiefs of Staff Gen. Martin E. Dempsey to arm carefully vetted rebels, a plan also backed by Clinton and then-CIA Director David Petraeus. Obama, however, warned it would increase extremism in the region.
A year later, Obama approved an effort to train and equip moderate Syrian rebels, though the move was widely criticized as too small to make a difference and fatally hamstringing the fighters by insisting they only target ISIS, not Assad's forces. Last month, the Pentagon paused the program after acknowledging that just four or five of the American-trained rebels are actually fighting.
Though the President can find backers of his policy on Syria inside the Beltway, he faces many critics who argue that he has not done enough to alleviate the crisis there.
Andrew Tabler of the Washington Institute for Near East Policy said Tuesday that the costs of the U.S. not acting in Syria are greater than the risks.
"President Obama and the administration waited too long to arm and organize the rebels and to enforce the red line on chemical weapons and look what happened," Tabler said. "Now before things get further out of control, they should seize the opportunity of for a limited no-fly zone."
He added, "There are large swaths of Syria that are not stabilized and we need to stabilize those areas and keep extremists out. Syria is going to keep hemorrhaging people and extremists until we do."