It is 10 years ago now that the younger Williams sibling confirmed her dominance of the women's game by completing her self-styled "Serena Slam" of winning four consecutive major championships with the 2003 Australian Open title, but as a new year begins the tennis community wonders whether it is about to witness a second coming.
In the preceding decade, Williams endured occasional bouts of injury, illness and indifference, which last year saw erratic early exits to Russia's Ekaterina Makarova in Melbourne and to Virgine Razzano in Paris. In that period, no woman had won back-to-back Grand Slams, let alone four-in-a-row, until last season, when Serena won Wimbledon and the US Open as well as an Olympic singles crown and a WTA Tour Championships.
Although a raft of plausible pretenders to her crown exist in the form of Viktoria Azarenka, Maria Sharapova, Agnieszka Radwanska, Angelique Kerber and home favourite Samantha Stosur, Williams is still the one who strikes fear into the rest of the women's locker room and she offers them little encouragement that they will be allowed in on the act any time soon.
Despite those two setbacks in the slams, Serena finished 2012 with a 58-4 record, losing only once after June, and there was no sign of her letting up when she took the title at the Brisbane International tournament last week to extend her run to 35 wins in her last 36 matches. No wonder she felt emboldened enough last week to talk openly not just about holding all four titles concurrently, but winning all four in a calendar year – a feat which would stretch her stranglehold over the slams to half a dozen tournaments. "I definitely feel that way," the 15-times Grand Slam winner said. "And I think maybe whoever wins the Australian Open will have that same thought [about a calendar year Grand Slam]. There is no way that Victoria or Maria or maybe some other players don't feel the same way."
Aged 31, victory at Melbourne Park could make her the oldest world No 1 since Chris Evert and, should she achieve that landmark, the ESPN analyst would lead the plaudits on her countrywoman's behalf. She believes Serena completing a perfect calendar year in the slams is a possibility and something that would consolidate her claim as being the best ever to play the game.
"Absolutely," said Evert. "The thing with Serena is not only her health but her motivation. I think she's got the motivation, there's no doubt about it, because she's been out of the game so many different times, either for injuries or for other interests in her life, so she's still a fresh older player.
"I don't think that motivation will be a factor, but to stay healthy in this day and age is, as we've seen with Rafael Nadal and other players, I think more difficult, especially for someone like Serena who is such a physical player and has a tendency to get injured.
"But when she is on, she is dominant and unbeatable. I don't know if anybody can really stop her. But you have to remember that we're talking Grand Slams in the same sentence, and they are two-week tournaments and have always provided surprises for us.
"There are no easy matches anymore, as we saw last year here when she lost, and also last year at the French when she lost. You have got to start at 90% to 100% from the first match. It is absolutely possible. But I have my doubts that it would happen ... only because she is human."
As Williams suggested, others may also envisage winning all four titles in a season, but making it happen is the hard part. While Sharapova capitalised on one Serena mis-step to capture Roland Garros last year, top of the list of pretenders is Azarenka, the reigning champion here and current world No 1. Unlike so many of the previous "pre-eminent" players in the world, the Belarusian is made of stern stuff and even had two championship points against Williams at Flushing Meadows.
But she has won just one of 12 tour meetings against Serena, and decided against risking another punishing loss when she withdrew from their semi-final in Brisbane last week after having part of the nail on her big toe removed following a faulty pedicure.
Expecting Laura Robson to figure in such exalted company isn't realistic or even fair, but at least for once a British woman features in the conversation about a forthcoming Grand Slam event.
The 18-year-old reached a first WTA Tour final in Guangzhou and showed enough poise against Kim Clijsters and Li Na at Flushing Meadows to hint at successes to come.
"There's no question Laura has the talent," said another ESPN pundit, Darren Cahill. "I don't think I've seen anybody in the ladies' game that varies the spin the way she can do it. The fact she is a lefty is a slight advantage going forward.
"She also understands the game extremely well and certainly has the weapons. But there's the court speed and the ability to play a little defensive tennis at times that is going to be important for her to evolve and improve."