Ansari revealed that he along with co-creator Alan Yang contacted the "Snowden" actor to do a cameo in the season two of the show, reported The Independent.
"I think we did go out to Cage and quickly received a '... No,'" IndieWire quoted Ansari as stating at an LA screening earlier this week.
The actor is the centre of one of season two's most memorable jokes - he's the star of the fake movie Death Castle - which features in the standout episode 'New York, I Love You.'
But "Brooklyn Nine-Nine" star Andy Samberg voiced Cage instead.
Emma Watson and "Fast & Furious" actor Tyrese Gibson feature in the fake movie within the episode.
The episode is notable for featuring a completely silent segment starring two deaf characters using only sign language.