Horne, a Republican elected in 2010, has proposed a voluntary program in which each school could nominate one employee to receive free firearms training by local sheriffs and the attorney general's office, Politico reported Thursday. The individual would be allowed to keep a weapon in a locked container at the school.
"The ideal solution would be to have an armed police officer in each school," Horne said in a statement Wednesday, but that may not be possible because of cost.
"In that case, the next best solution is to have one person in the school trained to handle firearms, to handle emergency situations, and possessing a firearm in a secure location," he said. "This proposal is analogous to arming pilots on planes."
Republican lawmakers in statehouses across the country have proposed allowing concealed carry of weapons on school grounds or arming some teachers following the Dec. 14 killing of 26 people, 20 of them children, at an elementary school in Newtown, Conn.
Teachers unions have fought such proposals, with two top national unions saying the focus should be on "ways to keep all guns off school property."
The National Rifle Association proposed placing an armed guard in every school across the country.
Arizona House Majority Leader David Gowan, R-Sierra Vista, said he would introduce the proposal, a release from Horne's office said.