The world number one defeated the Russian to win the Australian Open in January, and Sharapova admits that she would "love" to even the score.
"She beat me in Australia quite easily and I would love to get my revenge at a Grand Slam," she said.
"I'm so happy to get through this one," she added. "It has been so long since I have been to this stage at the US Open."
The semi-final between Sharapova and Azarenka is scheduled to take place this Friday.