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.
She feels that with age she is now better positioned to stay the course as defending champion in the second of the year’s four Grand Slam tournaments.
“I have tried to defend there (in Paris) once, twice, three times before. Didn’t quite work so well,” she said after winning the Italian Open on Sunday — her first title triumph in nine months.
“But this year is different. I’m going to definitely go in there and I feel more calm and I don’t feel stress to, like, have to win. You know, I feel like I just am happy to be out 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.”
– Emerging threat –
With two-time winner Maria Sharapova out of the picture under a doping cloud, the opposition to Williams is expected to come from Europeans in the shape of Germany’s Angelique Kerber, who upset Williams in Melbourne, two-time Wimbledon champion Petra Kvitova of the Czech Republic, 2014 finalist Simona Halep of Romania, Poland’s Agnieszka Radwanska, as well as Azarenka.
But there could be an emerging threat from her fellow American Madison Keys, who ran Williams close in the Rome final, and who seems to have developed a taste for claycourt action at just 21.
“I think having a couple of top 10 wins this week was really big for me and playing people who have done very well in Roland Garros and just on clay in general,” she said last Sunday.
“But I think the biggest thing is just how calm I have stayed on court and really, even in tough situations, stayed calm and collected and just really focused on my game, and I feel like I’m just playing much smarter tennis.”