Yes, there are Gray Foxes and kit foxes in the Arizona deserts
The arizona desert
There is no "Arizona Desert." However, there are three deserts that enter the state of Arizona - the Sonoran Desert, the Mojave Desert and the Chihuahuan Desert.
Arizona has the Chihuahuan Desert, the Sonoran Desert, the Mojave Desert and the Colorado Plateau Desert.
Arizona desert
The Sonoran Desert, the Chihuahuan Desert and the Mojave Desert all enter Arizona.
There are foxes that live in both habitats. The arctic fox is an example of a desert fox since the arctic qualifies as a desert habitat.
Arizona has true deserts. Alaska does not.
There are three deserts in southern Arizona: Chihuahuan Desert Sonoran Desert Mojave Desert
Arizona has the Mojave Desert, Painted Desert, Sonoran Desert and a small piece of the Chihuahuan Desert.
The Sonoran Desert, Mojave Desert and Chihuahuan Desert are all found in southern Arizona.
Most foxes that live in Arizona are Gray Foxes, Kit Foxes, and (although not considered to be a fox) Coyotes. Red Foxes live mostly everywhere EAST of the Rocky Mountains, with the exception of places like Texas and Florida. Parts of Arizona and a few other states have very few Red Fox. There are scattered but very few parts of Arizona that contain Red Fox.
Arizona is a desert but known to some as Indian land