The defending Wimbledon champion recently referred to Sharapova as "boring" in an interview with an American magazine and also criticised her boyfriend Grigor Dimitrov, who is rumoured to have previously dated Williams.
"She begins every interview with, 'I'm so happy. I'm so lucky.' It's so boring," the Daily Mail quotes Williams as saying. "She's still not going to be invited to the cool parties. And hey, if she wants to be with the guy with a black heart, go for it."
Sharapova is said to have retaliated by making reference to Williams's alleged relationship with her tennis coach Patrick Mouratoglu.
"If Serena wants to talk about something personal, she should talk about her relationship and her boyfriend who was married, who is getting a divorce and who has kids, and not draw attention to other things," said Sharapova.
On the court, Sharapova has not beaten Williams in nine years.