Christopher Traynor Fox, 39, of San Jose was in the Santa Clara County jail suspected of making telephone threats against a public official, the Chicago Tribune reported Friday.
Chicago police obtained a warrant for the arrest of Fox Tuesday and Chicago prosecutors planned to seek extradition, the Tribune said.
Fox's mother told a Chicago television station she thinks the alleged threat had something to do with remarks Daley made last week about gun control.
At a news conference about the possibility of the U.S. Supreme Court overturning Chicago's 1982 handgun ban, Daley was asked if the ban had been effective.
Picking up a rifle with a bayonet, Daley said, "It's been very effective. If I put this up your butt, you'll find out how effective it is. Let me put a round up your, you know."
Daley later apologized for the remark, the Tribune reported.