There's a running joke on the show that his character, Mike Chang, is tone-deaf and his dancing ability makes him valuable to the New Directions show choir.
In real life, Shum says he's been taking vocal lessons and hopes to get a shot at singing on the show.
"I'm not the best singer but I'm definitely not the worst. I'm somewhere in between but I'll let the audience gauge on how good that is and hopefully the show allows me to sing a real song," says Shum.
The character of Mike Chang was introduced in season one with very little dialogue.
Shum describes him as starting off as a background character who would dance and make facial expressions. He would be happy if the camera cut to him periodically for a reaction shot.
He's slowly gotten more screen time and was recently upgraded from recurring to a regular cast member.
As for his "Glee" co-stars, Shum says he's not sure if anyone will leave the series at the end of the third season. (There have been conflicting reports about some of the actors leaving the show because their characters graduate from high school.)
"I think we'll find out very, very soon but I think the main focus, instead of what's happening on season four, should be season three," says Shum.
"Glee" returns Sept. 21 on Fox.
Meanwhile, fans can catch "Glee: The 3D Concert Movie," in theaters beginning Aug. 12.