World No. 1 Williams, 32, has 17 singles majors on her CV and if she retains her French Open title she would join Evert and Martina Navratilova in second place on the list.
Despite being the wrong side of 30, Evert believes Williams is still improving on clay and is now prioritising grand slams rather than playing at full tilt at lower level events.
"I think she's peaked pretty well for the French Open," seven-times French Open champion Evert said during a conference call organised by broadcaster ESPN who she will be commentating for during Roland Garros.
"I think after the last two years of her playing more tennis than she's ever played, I think she came into this year exhausted. I think her priorities really are the grand slams this year. She knows what her place in history is now. She's gunning for those Grand Slam titles."
Williams was totally dominant last year, winning 11 titles including the French Open and the U.S. Open.
Last week she warmed up for her defence of the French Open by cruising to the claycourt Italian Open title in Rome, dropping only 22 games in the process.
"The French seems to be opening up for her. She has an apartment there. She lives there. She practises a lot there. Patrick (Mouratoglou), her coach, is French," said Evert.
"I think this tournament will motivate her. If she's healthy and fit, she's got it under control. She's learned to play on the clay a lot better from Patrick.
"She's improved her defence skills. She's always had the offence skills. She's more fit. She's moving better. She is patient with herself.
"She doesn't have to go for the winner on the fourth shot. She can wait eight or nine shots and go for the opening. She's more intelligent and thinking more clearly on the clay than she ever has."
Evert picked former French champions Li Na and Maria Sharapova as Williams's main rivals with another former winner Ana Ivanovic, who beat Williams at the Australian Open, back in the frame.
"She's beating some pretty good players," Evert said. "I like her attitude out there. You can tell she wants it. As far as winning a grand slam, I don't know.
"Anything's possible. I think realistically to be top five would be a better goal for her right now."
- Sports & Recreation
- French Open
- Martina Navratilova