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Hagel currently is the co-chairman of the president's Intelligence Advisory Board. Leon Panetta, who has been secretary of defense since July 2011, has indicated he wants to return to private life next year.

Four issues for the next term

When asked about his priorities for the next four years, Obama listed immigration, the economy, energy and debt reduction.

He will introduce legislation to fix a broken immigration system in 2013, he said.

"We have talked about it long enough," He said. "We know how we can fix it."

Obama also wants to fix America's infrastructure.

"If we are putting people back to work, rebuilding our roads, our bridges, our schools, in part paid for by some of these broader long-term deficit reduction measures that need to take place, that will grow our economy," he said

And he wants to increase further the amount of energy, especially green energy, that America produces.

"We are producing more energy and America can become an energy exporter. (The question is) how do we do that in a way that also deals with the environmental challenges that we also have at the same time," Obama said.

But the most pressing quandary is the fiscal cliff.

"It is going to be very hard for the economy to sustain its current growth trends if suddenly we have a huge bite taken of the average American's paycheck," he said.