Safarova believes the world No 1 can emulate Graf, Margaret Court (1970) and Maureen Connolly (1953) in landing the fabled foursome.
“Well, she’s a great player,” Safarova said after her excellent comeback ended 6-3 6-7 (2-7) 6-2 at Roland Garros.
“She has obviously the experience. She won those all grand slams already. I think she can do it. If she’s on her best and great shape, she’s playing the best tennis.”
Williams was overjoyed after overcoming illness, nerves and Safarova’s grit to win the last six games of the match.
“When I was a little girl, in California, my father and my mother wanted me to play tennis,” she said.
“And now I’m here, with 20 grand slam titles. This is very special for me. I haven’t always played very well here, but I’m really happy to win the 20th here.’’
Safarova was justifiably happy with how she played in her first major final, recovering from 1-4 in the second set and then surviving as Williams served for the match 6-5.
“I’m proud that I fought back in the second set, because it was looking like it will be an easy match,” she said.
“Serena was really strong out there. I just pushed myself to step up the level. Yeah, I fought. I did my best. It didn’t work out. I just couldn’t find any weapon that could stop her. But when she was on, she was just serving amazing and going for the returns, pressuring me right away. It’s just hard to do anything with that.”
At 33 years and 254 days, Williams is the second oldest grand slam winner in the Open era behind Martina Navratilova, who was nine days older at Wimbledon in 1990.
In adding a 20th major to a bulging collection of spoils, Williams moved into outright third on the highest grand slam winner’s list behind Court (24) and Graf (22).
The champion at Roland Garros in 2002 and 2012, Williams also owns six Australian Open, six US Open and five Wimbledon crowns.
The most dominant player in the world, the American has won the past three majors after failing at Wimbledon last year, when Petra Kvitova took the title.
The last player to win the US, Australian and French Opens in succession was Monica Seles in 1991-92.