The Italian set up the last-16 meeting with the world number two thanks to a victory over Dominika Cibulkova yesterday evening.
Despite admitting that Radwanska is a "great player", Vinci is adamant that she is in the right frame of mind to record a positive result.
"She's a great player," said the number 20 seed. "I'll have to play very well, but I'm feeling confident right now, so we will see what happens."
The 29-year-old's run at Flushing Meadows this year has been the furthest that she has ever gone.