Discussions about Clinton, D-N.Y., being asked to accept the post are "very serious," an Obama source says.
Sen. John Kerry, D-Mass., has been considered a leading contender for the post. But last week, ABC News' chief Washington correspondent George Stephanopoulos reported on "Good Morning America" that Clinton also was in the running to be Obama's secretary of state pick.
Though Clinton and Obama ran a contentious primary campaign for the Democratic Party's presidential nomination, Sen. Clinton and her husband, former President Bill Clinton, both campaigned for Obama in the general election campaign against the Republican nominee, Sen. John McCain of Arizona.
Asked if Hillary Clinton would consider the secretary of state job, a former official in President Clinton's administration said, "I think so. What would you rather do -- be senator or secretary of state?"
Asked about the reports on the Cabinet post and another report that Hillary Clinton went to Obama's home base of Chicago today, senior Hillary Clinton adviser Philippe Reines said, "Any speculation about cabinet or other administration appointments is really for President-elect Obama's transition team to address."
Pushed on whether she physically went to Chicago, Reines said only that she had no public schedule today.