Sheen invited the Rushmore star to join him and a few friends on a private jet bound for South America while they were working together on last year's (12) A Glimpse Inside the Mind of Charles Swan Iii - and Schwarzman admits he was initially keen to go and find out what his co-star's life was like away from the set.
He says, "I wanna seem cool, tough with him and I was like, 'Yeah, maybe, let me think about that'. Really, what I was thinking was, 'I gotta go home and I gotta clear this with my wife...'
"I go home and I say... 'Hey, funny thing happened today... Do we have plans this weekend, because Charlie Sheen asked if I would go with him to Colombia on a private plane. Should I go?' And she said, 'You've gotta be f**king kidding me. You are a father now, you've gotta be responsible. You could die down there.'"
But, despite the snub, mild-mannered Schwartzman and Sheen have become unlikely friends.
The Moonrise Kingdom star adds, "I love this guy a lot... I love the way he thinks, I love his mind. I love the way he speaks. He speaks in way that are sort of poetic and strange and beautiful, but I don't fully understand, literally, but I understand on a deeper level...
"One time he said, 'Hey, what's your favourite drink?' and I said, 'Gin'. And he said, 'Oh man, gin... The last time I drank gin I did a back flip off my bed into Mexico'."