Arpaio had toyed with running for governor in 1998, 2002 and 2006, but decided against it.
If Arpaio decides to run for governor, Arizona law would require him to resign immediately because he isn’t in the final year of his current term as sheriff.
The 77-year-old Republican has served five terms as sheriff.
Arpaio’s last campaign finance report showed he had raised $1.2 million in campaign money.
Candidates for governor include Democratic state Attorney General Terry Goddard and Republicans Gov. Jan Brewer, state Treasurer Dean Martin, Tucson attorney John Munger and Yavapai County businessman Buz Mills.