Among other Cabinet posts: senior Democrats say there is a strong possibility that Defense Secretary Robert Gates would stay temporarily and later give way to former Navy Secretary Richard Danzig. Even so, Republican Sen. Chuck Hagel of Nebraska and Democratic Sen. Jack Reed of Rhode Island also are said to be under consideration.
Democrats also say that several people remain in the running for Treasury secretary, including Timothy Geithner, president of Federal Reserve Bank of New York; Lawrence Summers, former treasury secretary and one-time Harvard University president; and former Federal Reserve Chairman Paul Volcker.
Several news organizations reported Thursday that Chicago businesswoman Penny Pritzker, who was Obama's national campaign finance chairman, was his leading choice to become secretary of commerce. However, Pritzker issued a statement Thursday saying she is not a contender for the post.
Officials say Laura D'Andrea Tyson, the former chair of White House Council of Economic Advisers under President Clinton, is in the running for the Commerce job.
The Obama advisers and Democrats discussed the Cabinet positions only on grounds of anonymity because of the private nature of the screening process.
Obama appears to be assembling a team that includes a mix of longtime aides, Washington insiders and a sprinkling of Democratic governors. Besides Napolitano, strong contenders for Cabinet posts include New Mexico Gov. Bill Richardson and Kansas Gov. Kathleen Sebelius.
Sebelius and Napolitano, who once was Arizona's attorney general, were among the first governors to commit to Obama's candidacy. Richardson endorsed Obama after ending his own presidential bid, angering Clinton and her husband, former president Bill Clinton.
As governor, Napolitano has fought to curb illegal immigration, but she has been skeptical that building a fence along the border will solve the problem. She once said, "You build a 50-foot wall, somebody will find a 51-foot ladder."
Last year, her state passed a law that requires all Arizona businesses to use the federal online database, E-Verify, to confirm that new hires have valid Social Security numbers and are eligible for employment. This has been a cornerstone of the Bush administration's immigration policy.
As governor she has overseen wildfires and severe flooding and worked with the Federal Emergency Management Agency, now part of the Homeland Security Department.