Word of the plan comes the same day Lt. Gov Gavin Newsom (D), a close Harris ally, said he would not enter the race. Harris and Newsom are both rising stars in California politics.
Boxer announced her plans to retire last week, setting of a scramble for her seat. Other Democrats have expressed interest in the race, including former Los Angeles mayor Antonio Villaraigosa. Another possible Democratic candidate is billionaire environmentalist Tom Steyer.
California uses an all-party primary system in which the top two vote-getters in the primary advance to the general election regardless of party affiliation.