We talked to people who work closely with DHS about who they see as the likeliest contenders. Below, we list the most prominent names mentioned, along with their advantages and potential downsides:
W. Craig Fugate, Federal Emergency Management Agency (FEMA) administrator
Few Obama administration appointees have drawn as many plaudits from both Republicans and Democrats as Fugate, who took over FEMA and turned the troubled agency into one that has responded to a series of disasters in a timely and efficient manner.
Mayorkas, who has headed the department's Citizenship and Immigration Services since 2009, is a Cuban-born lawyer who has won plaudits from a broad range of politicians and personalities, even Hollywood madam Heidi Fleiss when he was in the midst of prosecuting her as U.S. attorney for southern California. Janet Murguia, head of National Council of La Raza, said in an interview he would make an excellent pick, since "He is seen as a very credible leader, not only in our community, but in the field of law enforcement." And she noted that right now, "There are zero Latinos in the Cabinet."
John S. Pistole, head of the Transportation Security Administration
Pistole, a former deputy director of the FBI, has built good relations with Congress despite some lawmakers' concerns over recent proposed changes to screening procedures at airports -- particularly when it comes to knives.
Thad W. Allen, retired Coast Guard Admiral
Allen, who delayed his retirement to serve as the national incident commander during the 2010 BP oil spill in the Gulf of Mexico, served as a steady hand during one of the nation's worst environmental disasters in recent decades. He is well liked by members of both parties, and could win confirmation without a major struggle.
Kamala Harris, California Attorney General
President Obama caused a firestorm this spring when he called Harris "the best looking attorney general in the country." But Harris, who is African-American, is a serious politician who is seen as a potential gubernatorial candidate in her state, and has pleased liberals by furthering the cause of same-sex marriage.
David Heyman, DHS Assistant Secretary for Policy
Heyman is a respected expert on terrorism and critical infrastructure protection, who served on the Obama administration's transition team and was sworn into his current post on June 21, 2009. He has worked in the private sector as well as academia and other branches of government, which makes him an appealing candidate.
Joe Lieberman, former independent senator from Connecticut
Lieberman makes sense as DHS secretary for one pretty obvious reason: He created the department. Lieberman, as chair of the committee that is now referred to as the Homeland Security and Governmental Affairs Committee, drafted the bill that created DHS shortly after Sept. 11, 2001. He also recently retired from the Senate, meaning he's a free agent. But his tendency to give his Democratic colleagues heartburn may not make him an ideal fit.
Tony West, Acting Associate Attorney General of the U.S.
West, who is on the verge of becoming confirmed as associate attorney general after serving in that post since March of 2012, after heading the department's civil division for three years. A graduate of Harvard College and Stanford University, West is respected for his legal acumen and would add another African-American to the Cabinet if nominated and confirmed.
Richard Danzig, former Navy secretary
Danzing served in Bill Clinton's administration but also as an adviser to President Obama. He's currently head of the Center for a New American Security and serves on several pertinent boards of directors. Some see him as a top contender.
Ray Kelly, New York City police commissioner
Kelly has served in his post since shortly after Sept. 11, 2001, and also served in the Clinton administration. Despite his solid reputation, though, he has been critical in recent months of the Obama Administration's surveillance programs and for its posture toward New York's stop-and-frisk program. Given how pertinent those efforts are to the top DHS job, it may not be a great fit.
Joseph F. Bruno, commissioner of New York City Office of Emergency Management
Bruno has held several major positions, including New York City fire commissioner and state Supreme Court judge -- and there's a reason New York is home to a number of top DHS candidates, past and present: the city's high-profile security challenges.
Jane Harman, former Democratic congresswoman from California
Harman resigned from Congress in February 2011 to serve as head of the Woodrow Wilson International Center for Scholars. But she's clashed with House Minority Leader Nancy Pelosi (D-Calif.) in recent years, especially after Pelosi passed her over for the chairmanship of the House Intelligence Committee in 2007.
William J. "Bill" Bratton, former chief of police in Boston, Los Angeles and New York
Bratton has been the top cop in three of Americ'ns biggest cities because he's gotten results. He retired from the LAPD in 2009 and went into the private sector.
Jane Holl Lute, former DHS Deputy Secretary
Lute is a favorite of Senate Homeland Security Committee Chairman Tom Carper (D-Del.), but she recently departed (in April) to work on cyber security matters. The question is whether she would come back so quickly for the top job.
Rand Beers, Acting DHS Deputy Secretary
Beers was Under Secretary for the National Protection and Programs Directorate before replacing Lute in an acting capacity. He's close to Napolitano, a Vietnam veteran and a former longtime State Department employee. If the administration wants a seamless transition, it might be Beers (or Lute).
Jenny Durkan, U.S. Attorney for the Western District of Washington
Jenny Durkan, who serves as the U.S. attorney in Seattle and is openly lesbian, is also being looked at to replace Napolitano. She advises Holder on cyber crime issues and has some experience border issues given the fact that Washington state borders Canada. Members of the LGBT community are lobbying for her appointment, noting that Obama has yet to appoint a gay or lesbian Cabinet member.
Updated at 3:36 p.m.