The 37-year-old has won a record 23 grand slam singles titles in tennis’ Open era and could equal Margaret Court’s all-time mark with an eighth Wimbledon title in the next fortnight.
But Williams has struggled with injury this season, and King believes she needs to focus on getting fit.
“And at her age it’s much tougher, you’ve got to be smarter, you’ve got to get your nutrition right, you have to work harder. But it’s worth it if you want it. But if she doesn’t want it, it’s fine.”
However, her long-time coach Patrick Mouratoglou warns she should never been ruled out, especially at Wimbledon where she has won seven singles titles, the last of which came in 2016.
“With Serena, there is no rule,” Mouratoglou told CNN Sport at Roland Garros.
When asked if he was confident Williams could pass Court at this stage of her career, the Frenchman said: “Yeah, because you don’t want to go to 24 (and get stuck).”
Williams broke Steffi Graf’s Open-era grand slam singles record at the 2017 Australian Open, when she beat her older sister Venus for her 23rd grand slam title — while eight weeks pregnant.
But 2019 has been less successful so far.
After spraining her ankle during a quarterfinals defeat to Czech Karolina Pliskova at the Australian Open, Williams withdrew from a tournament in Miami in March with a knee injury that clearly hampered her movement during a straight-sets defeat to American teenager Sofia Kenin at Rolan Garros.
Although the chase for Court’s all-time slam record has been a key driver for Williams and her team in the past few years, some tennis watchers query its relevance.
Australia’s Court won 24 major singles titles between 1960 and 1973. She competed both in the amateur and the Open era, which began in 1968 when tennis turned professional.
However, Court won 11 of her titles at the Australian Open, during a time when not all top players made the long journey Down Under. Court also played during a time when it was not unusual for players to skip slams altogether because they could make more money on the women’s circuit.
“I don’t think it is a record she [Serena] needs, and I don’t think it is a record that she should be chasing,” WTA expert Courtney Nguyen said of Serena at the French Open. “I think that in a lot of ways her chasing the record, validates the record. When really the [main] record, it was Steffi’s record, which she already broke.
“When Steffi got 22, no one said, ‘Oh, you need two more to get to Margaret.’ It was just, holy crap, you are the greatest of all time, you have 22 majors. It’s a false record.”
‘Heaviness, stress, anxiety’
Although Williams and Federer, the men’s Open era record holder with 20 major titles, are both now in their late 30s, the two tennis superstars have a different mindset when they take to the court in the latter stages of their careers.
“Roger gets to plays freely in the last years of his career,” said Nguyen. “It is all a celebration, and he just gets to play, and there is a lightness around him.
“Whereas every time Serena takes to the court at a major, there is a heaviness, there is a stress, there is an anxiety, and that breaks my heart, because she is chasing a thing I don’t think she needs. And if she doesn’t get it, now that she has chased it, it feels like she is missing something.
“But she never needed it.”
When asked if the hunt for the all-time record was a burden for Williams, Mouratoglou said: “Whatever you are trying to achieve that is big, is possibly heavy. It’s big because it’s the record of all time and you have to set goals.”
Mouratoglou, who has guided Williams to 10 major singles titles since they started working together in 2012, said the attempt to break Court’s record is “really a source of motivation.”
“It’s difficult to reach it, the closer you get the more difficult it gets, as always,” he said.
“But now, for example, she’s not thinking about it. She knows she has this in her mind that she wants to achieve, but it’s not stressful. It might become when she gets closer to the finish line.”