The transition team has told Gen. Jim Jones that the post is his if he wants it, the sources told CNN, cautioning that no final decision has been made and discussions continue.

Conversations center on how much power Jones, who once served as NATO's operational commander, would have as national security adviser, CNN said.

One person close to the transition said Jones has a good relationship with current Defense Secretary Robert Gates, who could remain in that post, at least initially, after Obama takes office in January.