Robson, 19, eliminated Li in the third round at Flushing Meadows last year.
The fifth-seeded Li beat Sweden's Sofia Arvidsson 6-2 6-2 on Arthur Ashe Stadium court and Robson, seeded 30th, advanced with a 6-4 7-6 victory over Caroline Garcia of France, winning the second-set tiebreak 7-5.
"After last year I think both players improved a lot. I'm really looking forward to playing against her," Li told reporters about a rematch against former Wimbledon junior champion Robson.
"For sure, really challenging, a lefty, aggressive player. Also, I can prove myself after one year whether I can do better than last year."
Robson said she well remembered their showdown at the 2012 U.S. Open.
"I remember being so nervous when I walked on court," the Australian-born Briton said. "But just fighting through that and just sticking with her.
"I think she made a lot of mistakes in the first set, which helped quite a lot. Hopefully she'll do that again."
Li, 31, believes she has improved since taking on Carlos Rodriguez as her coach last year, although it has been a process.
"The first one or two months we have, he didn't talk too much, because he have to see what I'm doing," world number six Li said.
"After, I think especially in the winter training, we talk a lot. Not every day, but every second day we talk a lot to know each other pretty much," she added about Rodriguez, a former coach of seven-times grand slam winner Justine Henin.
"I was feeling pretty happy the way he is like now. We are communicating."
Li, a sporting trailblazer in China with more than 10 million fans on Chinese social media, said her relationship with a coach influenced more than just tactics and technique.
"I was feeling that a coach for me not only is about tennis coaching. He teaches me a lot like off of the court. He tells me a lot of experience, especially (for) press conference, communication with friends, with family, so many things."
(Editing by Greg Stutchbury)
