Clinton was rumoured last week to be a contender for the US's most senior diplomat, but talk had died down again after Democratic party activists questioned her suitability.
She is currently a US senator for the state of New York.
For 16 months, Clinton and Obama fought a sometimes bitter battle to secure the Democratic nomination for the presidency.
In June, she eventually conceded to Obama and urged her supporters to back him in the race for the White House.
Ahead of the Democratic convention in August there had been speculation that Obama might have tried to reach out to disgruntled Clinton supporters by inviting her to join him as his vice-president.
Obama instead chose Joe Biden, a fellow Democratic senator and a foreign affairs veteran - a policy area where Obama was seen as lacking experience.
The role of US secretary of state is the highest-ranking post in the president's cabinet and is fourth in line to succeed the president.
Clinton's husband, former president Bill Clinton, appointed Madeleine Albright as the first woman to become US secretary of state in 1996.