"A lot of people have talked to me about staying," Clinton, 64, told The Wall Street Journal.
She did not indicate how long she might stay in the Cabinet, saying it was "unlikely" recent events would delay her departure.
The Sept. 11 death of U.S. Ambassador to Libya Christopher Stevens and three other Americans at the consulate in Benghazi have left a cloud on Clinton's tenure at the State Department, the Journal said Thursday.
Her job approval rating was near 70 percent before the consulate attack, now acknowledged as an act of terrorism, and there had been speculation she might run for president in 2016, when she will turn 69.
Clinton has taken responsibility for what she called the "terrible events" in Benghazi but Obama said during his debates with Republican nominee Mitt Romney the buck stopped at his desk.
"Secretary Clinton showed leadership in acknowledging her ultimate responsibility for security failures," Rep. Darrell Issa, R-Calif., a harsh critic of the administration, said during congressional hearings, adding "such a willingness to take responsibility in this administration has been too rare."