Brennan, who spent about 25 years in the American spy agency, is expected to replace David Petraeus, who resigned last year upon admitting an extra-marital affair with his biographer and reserve Army officer Paula Broadwell, Fox News reported.
The CIA is currently led by Acting Director Mike Morell.
Brennan, who has served in the counter-terrorism post since the beginning of the Obama administration, had earlier been in the reckoning for the post in 2008, but withdrew amid questions about his connections to the techniques used by the agency during the administration of George W Bush.
The TV channel said Obama is planning a packed week of nomination announcements in the coming days, as he begins to roll out his second-term team.
Former Sen Chuck Hagel is expected to be nominated for defence secretary late Monday night. The president has already nominated Sen John Kerry for secretary of state.
Brennan also briefly served as director of the National Counterterrorism Centre during the Bush administration.