"I don't think that's going to define my career or make or break it," the No. 1-ranked American said.
In an exclusive interview this month at her Paris pied-a-terre two days after beating Lucie Safarova to win her third French Open and 20th major overall, Williams pooh-poohed the milestone on everyone's mind.
She is 14 matches away. Steffi Graf, in 1988, was the last player to win the Australian Open, French Open, Wimbledon and U.S. Open in a single season. No player has captured the first two legs since Jennifer Capriati 2001.
Williams, 33, said it would have preoccupied her in seasons past, but she has become so comfortable with her place in history, it matters little.
"I don't know how this sounds, but it's not on top of my list," she said, still sniffling from the flu-like illness that nearly derailed her run in Paris. "My list right now is to do well at Wimbledon. And then my list is to do well at the U.S. Open. And then Australia."
Williams, clad in shorts and an orange-and-white top with her Yorkshire terrier, Chip, nestled in her arms, added:
"I don't really think, nor am I overly concerned, about winning a Grand Slam at this stage of my career. I think five years ago - yeah. Ten years ago, yeah it might have. Now I've got enough. I don't need a Grand Slam to define my career whereas maybe a few years ago if I didn't have 20 Grand Slams then I would have needed that."
It makes sense that Wimbledon remains her immediate focus. The five-time champion has stumbled lately on grass. She lost to Sabine Lisicki in the round-of-16 in 2013 and to Alize Cornet in the third round last year.
"I haven't done well there in a while," she said. "I had done well for so long in the beginning of my career, and now it's just been like kinda shaky."
Still, Williams doesn't act like she's simply icing her career cake.
Though she is 32-1 in 2015, many of her matches have been drama-filled episodes where she has fallen behind, looked far from her best, and then lifted to another level and willed herself to victory.
She has bellowed "C'mons!", littered courtside mikes with F-bombs, and pleaded to the heavens and to her box, all in an effort to get her came on track.
Pam Shriver, the ESPN analyst, said Williams is probably of both minds.
"Athletes are gifted at taking bits of pressure off," said the former top-three player from Baltimore. "I don't disbelieve her, but I think deep down she wants to be one of the few players to go down with the calendar-year Slam."
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What isn't a matter of speculation: Williams, who turns 34 in September, is better than ever, and more distant from the field than at any time in her career.
Following an 11-month health and injury absence in 2010-11, Serena has been as close to untouchable as any player in history.
In 61 tournaments since June 2011, she has captured 30 titles, seven majors and compiled a .924 winning percentage (242-20). In the same number of tournaments prior to being sidelined, she won 11 titles, six majors and owned a .800 winning clip (180-45).
Her late-career success is the latest plot twist in a story of convention-breaking feats since she and her sister, Venus Williams, emerged from the tough streets of Compton, California, in the mid-1990s.
Serena returns to Wimbledon on the heels of another mini-comeback. When she departed London a year ago, she had failed to advance past the fourth round in three previous majors. And no exit was more bizarre than in London.
Three days after losing to France's Cornet, a dazed Serena flailed around the court in a doubles match with Venus before retiring. Speculation about what ailed her was rampant. But Williams rebounded as only she can.
She lost just once the rest of the season (not including a withdrawal and a retirement), captured the U.S. Open, and with her two majors in 2015 is now on the cusp of a second "Serena Slam" - holding all four majors simultaneously.
Serena won four consecutive Grand Slams in 2001-02 when she was 21.
"What a turnaround that is," said Shriver.
If Serena arrives in London as a heavy favorite once again, her rivals have aided her domination. Reigning Wimbledon champion Petra Kvitova of the Czech Republic, ranked No. 2, has struggled with her health and top form. The 2011 and 2014 Wimbledon champion withdrew from this week's warm-up event at Eastbourne with an illness.
Last year's finalist Eugenie Bouchard and 2012 runner-up Agnieszka Radwanska are mired in slumps. Third-ranked Simona Halep and No. 5 Caroline Wozniacki have yet to approach last season's high levels.
Then there is Maria Sharapova. The five-time Grand Slam champion from Russia, who shocked Serena in the 2004 Wimbledon final, hasn't beaten her in more than a decade and is 2-17 overall.
"No one really pushes her," said former No. 1 Justine Henin of Belgium, who was 4-3 against Williams at majors. "A few girls took some sets but it seems like even mentally it's still very hard for the girls to go to the next step."
The 5-foot-6 Henin, who retired at 28 in 2011, is impressed by Serena's longevity, durability and motivation. She said Graf's Open-era mark of 22 majors, which the American could tie at the U.S. Open, and Margaret Smith Court's all-time record of 24 are "in danger."
"Serena has the physical capacity to be there a long time," said Henin, a seven-time major winner. "Mentally, it looks like she wants to be."
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Like the ageless Martina Navratilova, who advanced to the 1994 Wimbledon final at age 37, Serena is leaving no stone unturned as she winds down her career.
Three years ago, she went outside her close-knit family for coaching help and enlisted Frenchman Patrick Mouratoglou. She sharpened her diet and attitude. She stepped up her off-court fitness with fitness guru Mackie Shilstone.
With Mouratoglou, Serena has won seven of the last 12 majors and become a more well-rounded player at a time when most are fading away.
"What's most impressive is that he really has a way to motivate me," said Serena.
She also said the health scare four years ago transformed her.
"Before, if I lost I would just be devastated," she said. "I was inconsolable and blah, blah, blah. After that, things could be worse than losing a tennis match."
But with age comes new challenges. In Australia, Serena spoke of battling nerves in surviving several wobbly matches on her way to a sixth Melbourne title in January. At Roland Garros, she battled through five three-set matches, her most at a major.
"It's not her best level but it's good enough to almost not lose a match for six months," said Mouratoglou in an interview this month. "I'm okay with that level."
Some observers believe that Serena is less comfortable on grass than hard courts, where she can set her feet before ripping into her shots. She's also less reliable at the net, which is more of a factor on grass.
Perhaps the biggest hazard to Williams is that she knows the speedy courts at the All-England Club benefit her big serve and first-strike aggression. When she doesn't dominate, it rankles.
"On paper she should just breeze though every Wimbledon," says 18-time major winner Chris Evert.
Serena agreed.
"It's not my favorite surface, which is weird," she says. "It never has been. But it does suit my game."
Serena is proud that she is already holding three majors with a shot for a fourth - 12 years after she first ran the table in a non-calendar year. "Those kind of feats mean a lot to me," she said.
Maybe she has hit on the right formula, paradoxical as it seems on the surface. She can tell herself it's all gravy now, and as long as she avoids the pitfall of disengaging too much of her ego, she can relax. That can be a fine line to straddle.
"I'm not thinking about it," she insisted once again about winning all four majors. "I don't want to think about it. I'm more focused on the Serena Slam. Well, forget all that, I just want to do well at Wimbledon."
Do you believe her?
- WASHINGTON POST-BLOOMBERG