Williams, who will turn 36 later this month, was admitted to the St Mary’s Medical Center in West Palm Beach, Florida on Wednesday before going into labor overnight.
There was no immediate confirmation of the birth from Williams’ representatives.
Elder sister Venus Williams described herself as “super excited” after being informed of the reports concerning the baby as she walked on to the court for her third-round match at the US Open in New York.
However she declined to take questions on the subject in her post-match press conference.
“I’m definitely available to answer questions about tennis. That’s all right now,” Venus told reporters.
Earlier, a producer with the Florida-based WPBF television station cited hospital sources as saying Williams’ daughter weighed in at six pounds and 13 ounces (3.09 kilograms). Celebrity magazine US Weekly cited an unnamed source close to the tennis star confirming the birth.
Williams, who is engaged to Reddit co-founder Alexis Ohanian, was swiftly greeted with an avalanche of congratulations from well-wishers.
“Congrats Serena!!! So much joy for you!!!” Spanish star Rafa Nadal wrote on Twitter.
Pop diva Beyonce took to Instagram to send her message, posting a portrait of a pregnant Williams in a flowing white gown with the message: “Congratulations Serena!”
Williams’ coach Patrick Mouratoglou added on Twitter: “Congratulations @SerenaWilliams for your baby girl. I am so happy for you and I feel your emotion. Recover well & enjoy without limitation.”
US tennis legend Chris Evert meanwhile chimed: “I’m so thrilled for her. And what a role model she’s going to be for her daughter.”
Media reports said 23-time Grand Slam singles champion Serena — who revealed she was pregnant in April — was induced overnight Thursday.
Other fans meanwhile wasted no time in anointing the tennis star’s daughter as a future champion.
“Hello to the future queen of tennis,” one post on Twitter read. “A future champion is born,” added another.
Those sentiments sparked light-hearted alarm for Spanish star Garbine Muguruza. Told that Williams’ baby is a girl, Muguruza replied: “Well, I hope she doesn’t play tennis.”
– ‘Outrageous’ goal –
Williams has vowed to return to competitive tennis in January to defend her Australian Open title, which she won while newly pregnant.
Williams last month told Vogue in a wide-ranging interview that she had set herself a goal of returning to play in Melbourne at next year’s Open.
“It’s the most outrageous plan,” she said. “I just want to put that out there. That’s, like, three months after I give birth. I’m not walking anything back, but I’m just saying it’s pretty intense.”
Williams’ coach Mouratoglou meanwhile joked Friday that he expected to hold the tennis star to her word.
“Btw @serenawilliams I wish you a speedy recovery… we have a lot of work ahead of us,” Mouratoglou wrote in a Twitter post.
Williams also revealed in her Vogue interview she had long suspected she would give birth to a girl.
“Two weeks after we found out (about the pregnancy), I played the Australian Open. I told Alexis it has to be a girl because there I was playing in 100-degree weather, and that baby never gave me any trouble. Ride or die. Women are tough that way,” Williams told the magazine.
A separate article in Vanity Fair in June said Williams, who unveiled her pregnant body in a nude cover photo for the magazine, planned to tie the knot with Ohanian later this year after the birth. The couple announced their engagement in December after meeting in 2015 in Rome.
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