John Mulaney could be the next breakout star of “Saturday Night Live.” The only problem: Most people who watch “SNL” don’t know who John Mulaney is.

A writer for the sketch show since 2008, Mulaney has appeared on-screen only a handful of times. His greatest contribution to the series is Stefon, Bill Hader’s uber-hip nightlife correspondent, who Mulaney helped create.

Outside of 30 Rock, Mulaney tours often doing stand-up. “New in Town,” the 29-year-old’s first hour-long Comedy Central special, debuts Saturday at 10 p.m. (and on DVD and CD Jan. 31).

In the special, which will be familiar to those who saw the Georgetown alum at the DC Improv last summer, Mulaney riffs on his awkward adolescence, “Law and Order: SVU” and why he gave up drinking at 23.

Mulaney’s jokes are witty but deceptively simple. Example: “I was once on the telephone with Blockbuster Video, which is a very old-fashioned sentence,” Mulaney remarks, setting up another bit.

With his boyish looks and agreeable persona, it won’t be long before Mulaney is on TV regularly. The only question is: Will it be on “SNL” or somewhere else?