These adviser cautioned that no final decision has been made on the position, which involves directing the massive department created by Congress in the wake of the Sept. 11, 2001 terrorist attacks on the United States.
The adviser agreed to discuss the situation only on grounds of anonymity because of the private nature of the screening process for Obama's Cabinet. Napolitano, who once was Arizona's attorney general, was among the first of the Democratic governors to commit to him.
Several news organizations reported Thursday that Chicago businesswoman Penny Pritzker, who was Obama's national campaign finance chairman, is his leading choice to become secretary of commerce. But the Obama adviser disputed the reports.
Among the names being bandied about as the Obama transition team sets up the new government are several people with long careers as Washington insiders, notwithstanding Obama's clarion call in his campaign for change in the nation's capital.
Obama, for example, is enlisting former Senate leader Tom Daschle as his health secretary. Hillary Rodham Clinton seems more likely than ever to be his secretary of state. Clinton is deciding whether to take that post as America's top diplomat, her associates said Wednesday.
And Obama is ready to announce that his attorney general will be Eric Holder, the Justice Department's No. 2 when Clinton's husband was president. Rahm Emanuel, Obama's chief of staff, is another veteran of the Clinton White House.
As a border governor, Napolitano has fought to curb illegal immigration, but 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 also overseen wildfires and severe flooding and worked with the Federal Emergency Management Agency, which is now part of the Homeland Security Department.
Daschle's selection to head the Health and Human Services Department - confirmed Wednesday but not yet announced - isn't at the same level of Cabinet prestige as the top spots at the State and Justice departments. But the health post could be more important in an Obama administration than in some others, making Daschle a key player in helping steer the president-elect's promised health care reforms.
Daschle could push Obama for quick action on health care reform next year, if he follows his own advice.
The former South Dakota senator said efforts during the Clinton administration, led by Mrs. Clinton, took too long and went into too much detail, giving every interest group an opportunity to find something they didn't like about the plan.
"The next president should act immediately to capitalize on the goodwill that greets any incoming administration. If that means attaching a health care plan to the federal budget, so be it," Daschle wrote in a book he released this year, "Critical: What We Can Do About the Health care Crisis." "This issue is too important to be stalled by Senate protocol."
Daschle's return to the government will be a vindication of sorts. He was the Senate Democratic leader when he was defeated in 2004 by Republican John Thune, who convinced voters back home that Daschle was more concerned with Washington than with them.
In fact, Daschle stayed in the capital city after his defeat, becoming a public policy adviser and member of the legislative and public policy group at the law and lobbying firm Alston & Bird. Daschle isn't registered as a lobbyist. He advises clients on issues including health care, financial services, taxes and trade, according to the firm's Web site.
Health care interests, including CVS Caremark, the National Association for Home Care and Hospice, Abbott Laboratories and HealthSouth, are among the firm's lobbying clients.
Daschle's appointment was not formally announced, but Democratic officials said the job was his barring an unforeseen problem as Obama's team reviews his background. One area of review will include the lobbying connections of his wife, Linda Hall Daschle, who has worked mostly on behalf of airline-related companies over the years. The officials spoke on condition of anonymity because they weren't authorized to discuss the matter publicly.
Republicans sniped at what they saw as an unwelcome trend. Alex Conant, spokesman for the Republican National Committee, said, "Barack Obama is filling his administration with longtime Washington insiders."
Associated Press reporter Eileen Sullivan in Washington contributed to this story.