The show will air as part of a new run of stand-up specials on the radio station in the autumn.
A Small Talk About Small Talk is described as a show that "unpacks the various things that go on in our heads while we're wading through the quicksand that is polite chit chat."
Norris, who won Best Show in the Comedians' Choice Awards at the Edinburgh Fringe last year, says: "I'm really looking forward to taking thoughts from the stage and translating them for a radio audience and playing with sound in the same way I would normally play with images in my live shows."
The episode is being made producer Steve Doherty from Giddy Goat Productions. Norris and Giddy Goat recently collaborated to record the show Joz And Roxy Are Useless Millennials, which was broadcast in February.
A Small Talk About Small Talk is expected to be recorded in the autumn.
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