The Estonian world number 46 booked her place in the last 16 of the tournament with a victory over American wildcard Alison Riske on Saturday, while Robson came from behind to defeat New Zealand's Marina Erakovic.
"It's not scary," Sky Sports News quotes Kanepi as saying. "I actually like to play more on the big courts than on the small ones because then I feel like I'm playing a real tennis match. I like it. All the crowd will be against me, but I think I'm going to enjoy that."
The match marks the first time that Robson and Kanepi have met on the WTA tour.