The actor told TV Guide that he enjoys the "odd couple" relationship between the duo and explained that there is "something very funny" about them.
"Elijah is the sadistic, quiet, calm zinger-type comedy," he said. "Whereas Damon [Ian Somerhalder] is this snarky, sometimes bitchy and tempestuous vampire."
However, Gillies added that he would love to see more scenes between Elijah and Klaus (Joseph Morgan), saying: "I just feel like if [they] could ever solve their differences, the world would be theirs."
Gillies also joked that viewers like Elijah because when he arrives people "know things are going to happen", adding: "When he turns up he's exposition and movement and the story is taking flight - or maybe fans just like his multiple haircuts."
The Vampire Diaries returns with a new episode in the US on March 15 on The CW. The show airs in the UK on Tuesdays at 9pm on ITV2.