A Special Weapons and Tactics (Swat) veteran from Phoenix, Sean Truelove, has researched the possibility of landing a $100,000 federal grant to fund a pilot programme to train one monkey.
"Everybody laughs about it until they really start thinking about it. It could change the way we do business," he said.
Major city police departments in the US use paramilitary Swat teams for hostage situations and in situations involving heavily armed criminals.
Truelove told local newspapers the idea came to him in a dream about 18 months ago.
The test monkey could be trained to unlock doors and search buildings for police on command, Truelove said.
The capuchin monkey is considered one of the smartest primates, known by many for its decades-long association with organ grinders. A capuchin monkey weighs 1.3 to 3.5kg and lives 15 to 20 years.
Capuchin monkeys, native to southern central America, have been used to help disabled people, and are able to perform such tasks as retrieving items, serving food and opening and closing doors.
The Arizona police department issued a statement saying: "We have always encouraged our department members to seek creative and innovative ways to improve public safety in our community."
"I've always heard you can train a monkey to do anything. Does this mean he's going to have on little black fatigues?"
National Tactical Officers Association board member
But the department also said the idea of training a capuchin Swat monkey had not been cleared by the department's executive ranks.
A representative from the nation's largest association of Swat officers also could not resist poking a little fun at the proposal.
"I've always heard you can train a monkey to do anything," Steve Smith, a board member of the National Tactical Officers Association, said when reached at a convention in Nashville.
"Does this mean he's going to have on little black fatigues?"