Zachary Running Wolf, an activist who opposes the University of California, Berkeley's plan to tear down trees next to the university's football stadium to build a new sports training facility, also has taken out papers.
Wolf finished a distant third in the 2006 election with less than 5 percent of the vote.
Bates, who defeated Dean in the 2002 election and formerly served in the state Legislature as well as on the Alameda County Board of Supervisors, was re-elected in 2006 with more than 62 percent of the vote.
His chief of staff, Julie Sinai, said Bates plans to run for re-election again and will formally announce his plans at a news conference on Monday.
Dean served two terms as mayor and a total of 15 years on the Berkeley City Council before Bates defeated her by a margin of 55.4 percent to 42.9 percent in 2002.
The 2002 campaign was marred by an incident in which Bates trashed about 1,000 copies of an edition of the Daily Californian, the university's student paper, that contained an endorsement of Dean.
On Jan. 8, 2003, Bates pleaded guilty to a petty theft infraction and was fined $100.
Bates also agreed to pay $500 restitution to the Daily Cal.