The two met in June when Burke hosted the 2012 NHL Awards and they stepped out for the first time as a couple at a charity event Wednesday, People magazine reported.
Lupul told the Toronto Sports Network he looks for a sense of humor in a perspective girlfriend.
"But she has to be a genuine person -- someone you can talk to and enjoy being around," he said.
In the same interview, Lupul admitted to teaching himself the guitar in his spare time and on occasion, using his fame to get perks.
"I'll be honest, I've snuck [in a namedrop] a couple of times," Lupul said. "Maybe like if a place is super lined up -- I hate doing this -- but if a place is super lined up, I'll be like, 'Hey, bro, I play for the Leafs. Any chance I can slide in there?' And usually it works. But still, it's a little embarrassing to do, too."