"They started dating after meeting through friends recently," a source told Life & Style.
"He's super busy rehearsing for his Big Time Rush tour, which [kicked] off [February 6], and she's gearing up for the next season of DWTS. They're both really busy, but they enjoy each other's company."
Rumors of an alleged romance first sparked after the pair was reportedly spotted dining at The Real Housewives of Beverly Hills star Lisa Vanderpump's SUR restaurant in West Hollywood on Tuesday.
"They made time in their schedules for the dinner, and really hit off," added the source. "It's going to get serious soon!"
When they were photographed at SUR, Murgatroyd, 27, and Maslow, 23, were wearing matching black leather jackets.