It comes as the Secretary of State prepares to step down from her role.
Obama stated the reason for the interview was to publicly thank Clinton for her work, describing her as "one of the finest Secretary of States" the US has had.
Asked whether the praise could be seen as an endorsement for a run by Clinton in the 2016 election, Obama responded: "You guys in the press are incorrigible. I was literally inaugurated four days ago and you're talking about elections four years from now."
Clinton added: "The president and I care deeply about what's going to happen for our country in the future and I don't think either he or I can make predictions about what's going to happen tomorrow or the next year."
The Secretary of State was also asked about her health in the interview, which she described as "great".
Clinton was admitted to hospital in December due to a blood clot following concussion:
Clinton is to be replaced by Senator John Kerry as Secretary of State. Foreign Secretary William Hague will mark her departure on Monday night by hosting a farewell party for her in Washington.
Hague is due to preside over a private dinner for his opposite number during a visit to the US capital where he is expected also to hold meetings with officials, politicians and business leaders.