But to do so, the 34-year-old American will have to achieve something she has so far failed to manage — defend her crown in Paris.
Just three of Williams’ 21 Grand Slam titles have come in France — the first in 2002 and then a long gap until 2013 and 2015.
The year after her inaugural French Open title, she lost in three tough sets to eventual winner Justine Henin — hardly a major upset at that time.
But in 2014 she lost a second round tie to young Spaniard Garbine Muguruza, a defeat that recalled her shock first round exit at the hands of Virginie Razzano two years previously.
That defeat to the lowly-ranked French player resulted in Williams re-dedicating herself to the game under the guidance of French coach Patrick Mouratoglou.
The result has been spectacular with her winning two Wimbledon titles, three consecutive US Opens between 2012 and 2014, one further championship in Paris and the Australian Open in 2015.
Williams, who won her first title in nine months in Rome last weekend, will begin her Paris defence against Slovakia’s Magdalena Rybarikova, the world number 76, who has yet to make it beyond the second round.
The American star insists she is feeling no pressure.
“I think now it’s different because I want to win more than I think most people ever, but also I think it’s different now because I don’t have anything to prove and I don’t have anything — it’s just a different feeling,” she said.
“Whereas five, ten years ago, oh, I’m defending and I feel that pressure. Now it’s like I’m defending, I’m in Paris, it’s cool, and I’m having, you know, the time of my life. I’m just happy to be here.”
The victory in Italy came at an opportune moment for Williams as she had gone title-less since Cincinnati in the buildup to last year’s US Open.
There then followed losses in the finals of the US and Australian Opens and a defeat to main rival Victoria Azarenka at Indian Wells.
A fourth round loss to Svetlana Kuznetsova at Miami saw Williams pull down the shutters for a while only for her to roar back to form in Rome.
Asked how relieved she felt to finally get another win — the 70th of her career — under her belt Williams replied: “It feels great. But I mean, I have played, let’s see, US Open, Australian, Miami, Indian Wells. So it’s only four tournaments. So it’s not like I was playing every week.”