Rahm Emanuel, the White House chief of staff, could announce by the end of this week whether he's leaving his job, NBC News reported Monday.
Emanuel is weighing a run for mayor of Chicago.
A source close to Emanuel said an announcement could come as early as Friday but no final decision has been made because of family considerations, according to NBC News.
Earlier Monday, President Barack Obama said: "I think that Rahm will have to make a decision quickly because running for mayor in Chicago is a serious enterprise."
Obama has said Emanuel, a Chicago native and former congressman, would be "a terrific mayor." Longtime Mayor Richard Daley isn't running again.
Mayoral candidates need 12,500 valid signatures to get on February's ballot.
Several media reports said Emanuel was likely to step down — or was at least considering such a move — before U.S. congressional elections on Nov. 2.
White House spokesman Robert Gibbs said earlier Monday that Emanuel was still "in the process of thinking about what he's going to do next."
"I'm not going to rule anything in or anything out," Gibbs said aboard Air Force One on the way to New York, when asked if he could exclude the chance of Emanuel leaving in October. "He's in the process of thinking through what's best for Rahm."
Emanuel's family only moved to Washington recently, and his children started school in the area just three weeks ago.
Emanuel's current post gives him influence in shaping Obama's legislative priorities. He also oversees White House staff and effectively determines who sees the president.
If Emanuel were to leave, Obama adviser Pete Rouse would be widely expected to step in on an interim basis.
Among those mentioned as possible replacements are Obama adviser Valerie Jarrett; deputy national security adviser Tom Donilon; Ron Klain, who is Vice President Joe Biden's chief of staff; White House Counsel Robert Bauer; and perhaps even Rouse himself.
POLITICO reported Tuesday that former Senate Majority Leader Tom Daschle and CIA director Leon Panetta could also be in the running.
If Emanuel, a Democrat, decides to run for mayor, he has until Nov. 22 to file for a Feb. 22 primary election. He would also need to organize a campaign and start raising funds.
Known for his political acumen, aggressive style and expletive-laced language, Emanuel represented a Chicago district in the U.S. House of Representatives before joining Obama's team.
Obama arrived in Albuquerque, N.M., on Monday evening, the first stop on a multi-state trip to discuss issues with voters and rally supporters on behalf of Democratic candidates. He is scheduled to also visit Wisconsin, Iowa and Virginia before returning to Washington on Wednesday.