Both actors provide their voices in Wes Anderson's stop-motion animation Fantastic Mr Fox.
Schwartzman told Parade: "Typically when you're working with someone it's not kosher to just kind of gaze at them because you're usually on camera as well.
"But when we were sitting around a table with just a recorder, it was really nice for me to be able to look at George. I admit I might have actually been staring."
He added: "Obviously, he's a handsome gentleman, but what I found fascinating was just kind of watching him work. It was like having a front row seat in an acting class."
Schwartzman also confirmed that Anderson had encouraged the cast to interact with each other and took them on a field trip to a farm where they "ran around and played in the dirt and did all sorts of crazy things".