The move would involve every community and roughly 2,000 schools across the state.
Horne's idea, a bill, sponsored by State Representative David Stevens of Sierra Vista, would have one person designated by the school's principal to be armed.
"This individual would volunteer and be trained by law enforcement," said Horne Monday afternoon. "We would train them not only in marksmanship, but in good judgment, when to shoot, when not to shoot."
The training would be paid by the state but the individual would carry their own gun.
Horne told ABC15 the gun would be locked away from children.
"The idea is having the gun locked so that kids can't get to it, but it's quickly available if someone needs it," said Horne. "I saw some people say that we should let any teachers bring guns to school which I think is a mistake because you could have an accident."
Many details are expected to be released during a news conference on Tuesday, but Horne told ABC15 he's prepared for any backlash.
"I have four children, I understand their (parents) concerns," said Horne. "We need to do something so that if a bad guy gets into a school there's someone there to stop him."
Horne said the volunteer assigned to the task would remain a secret and the location of the gun would be confidential as well.
He went on to tell ABC15 this move is actually his second choice.
"I would prefer school resource officers, but with dwindling budgets that cannot happen, so this is the best alternative."