By Will Swanton
NEW YORK (Reuters) - Serena Williams enters the second week of the U.S. Open believing she cannot be considered the greatest of all time unless she wins the most major championships.
The most dominant player of her era, America's world number one will meet Spain's 18th-seeded Carla Suarez Navarro in the quarter-finals of the U.S. Open on Tuesday.
The 31-year-old Williams has won 16 majors to trail Margaret Court (24), Steffi Graf (22), Helen Wills Moody (19), Chris Evert (18) and Martina Navratilova (18) on the all-time list.
"I go by the numbers," Williams said. "I don't think I'm the greatest, because Steffi has way more majors than me. I just go by what's written down. I would not put me as the greatest. You still have Steffi and all those other women that have way more grand slams than me."
Williams is a headline act of the U.S. Open and arguably the most famous female athlete in the world. But she denied part of her mission against Suarez Navarro would be to entertain.
"I'm literally going out there to play, I'm not thinking about being a star," she said. "I don't go out there thinking like that.
"I just want to play tennis and I want to do really good at it. It's not about the stage for me. It's just about getting that ball in."
The other quarter-final on Tuesday will place China's fifth seed Li Na against 24th-seeded Russian Ekaterina Makarova.
An all-Italian affair between Roberta Vinci and unseeded Flavia Pennetta will be staged on Wednesday with the last quarter-final between Slovakia's Daniela Hantuchova and either Victoria Azarenka or Ana Ivanovic.
The round of 16 match between Azarenka, the second seed from Belarus, and Serbia's 13th-seeded Ivanovic was postponed on Monday because of rain.
(Editing by Gene Cherry)