An administration official the Post described as familiar with Obama's thinking on the matter said Rice, 48, is the front-runner to succeed Thomas Donilon in the position this year.
Rice had been touted as a likely nominee for secretary of state, but Obama never put forth her name after congressional Republicans pounced on her for comments she made about the attack on the U.S. Consulate in Benghazi, Libya, last September. That job went to John Kerry instead.
The national security post, however, would put Rice near Kerry in helping shape Obama's foreign policy.
The Post said Rice's U.N. colleagues anticipate she probably will be appointed sometime after the United States assumes the rotating presidency of the U.N. Security Council in July. The adviser's position does not require Senate confirmation.
"I think that Susan always maintains close relations with the president and his national security team, and that continues to be the case," Ben J. Rhodes, spokesman for the National Security Council, told the newspaper. "If anything, the way she handled the Benghazi situation -- and then the withdrawal -- only enhanced her relations here, because she did so with grace and good humor."