The couple will perform two dances on tonight's (Monday) edition of the ABC competition, tackling the quickstep and the insta-jive.
Writing in her People blog, dancer Burke said: "He's not really nervous about the end of the competition, but he just really wants to make it to the finals.
"It's already week eight. He's doing everything in his power to stay in this. I really can't believe there are only two weeks left."
Burke went on to say that she wants Kardashian to "ham it up a little bit more" on television so that his personality really shines through to the audience.
"I think he'll do well as long as he brings the energy and it really comes through in his personality that he's having fun and stuff like that," she wrote. "I think the whole personality thing has been a challenge for Rob on the show.
"He's such a great guy with a fun sense of humour."
Kardashian's mother Kris Jenner recently said that Dancing with the Stars had boosted her son's self-esteem and praised the show for giving him the chance to shine in the limelight away from the shadow of his famous sisters.
Kardashian and Burke scored 25 out of a possible 30 points for their tango to the theme from The Addams Family on last week's Halloween-themed episode of Dancing with the Stars.
David Arquette became the latest celebrity to exit the competition following his performance, leaving just Kardashian, Nancy Grace, JR Martinez, Hope Solo and Ricki Lake in the running to win.
Dancing with the Stars airs Mondays and Tuesdays on ABC.
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