"I don't. I'm terrified, to be honest. It would just be a really bad situation if that was me," Williams said Thursday afternoon. "Plus, my sister [Venus] went through a lot of illnesses and with her going through that, she was able to introduce me into a really vegan and raw, kind of really vegetable, whole raw world that I really enjoyed. And I was able to see a lot of benefits in my game and my body in general from that.
"Just even from a health perspective, I've never been a big fan of taking anything."
While Williams said she was "shocked" and as surprised as everyone else by the Sharapova news, Andy Murray said the news of another athlete doping was not shocking to him.
"The stories like this happen regularly now in sports -- it seems like it's almost a weekly occurrence. So I wouldn't say it was shocking, really," he said, adding, "I read that 55 athletes have failed tests for that substance since January 1st. You just don't expect high-level athletes at the top of many different sports to have heart conditions."
Asked what punishment Sharapova should receive for taking meldonium, Murray said: "That's not up to me to decide, but if you're taking performance-enhancing drugs and you fail the drug test, you have to get suspended."
Murray said it is wrong to take a prescription drug to enhance performance if the drug is unneeded. "You're just using it for the performance-enhancing benefits that drug is giving you, and I don't think that's right."
He also said he thinks the International Tennis Federation needs to do more to prevent doping.
"I think all sports can do more," he said. "I think it's better than a few years ago. Last year, I certainly got tested a lot, but this year I've been tested twice so far and we're three months into the year, whereas last year I got tested loads. But this year to get tested twice three months into the year is clearly not enough."
Serena Williams said she had never heard of meldonium. "I'm studying medicine but I've never heard of it. Maybe I'm not studying hard enough."
Is Williams worried the integrity of tennis is threatened by this latest news, in addition to the recent match-fixing allegations?
"The majority of the players play with integrity. They do things when they're out there because they want to be the best they can the right way," she said. "It's just like the world. We live in a massive world with billions of people, and there are a few people who do things and it makes people scared, but that doesn't make the whole world a bad situation and a bad place.
"That's the same thing with tennis. The majority of players here, for years and years and years, really pride themselves on having integrity and playing with that. I think that beyond these two situations, we're still out there and we're still working hard."
WTA CEO Steve Simon said that while no one wants to see a player test positive, drug testing is necessary.
"Anti-doping is in place for a reason, [Sharapova] did test positive and there is no player that's above the rules, and she will go through the process and whatever the process determines we will support," Simon told ESPN. "We have to have that integrity in our game and anytime someone becomes bigger than the rules, that's not going in the right direction."
Simon did, however, credit Sharapova for accepting responsibility for her actions.
"It was obviously very sad and terrible news to receive. And Maria has been somebody that I think has conducted herself with the highest level of professional integrity in the game, and I think that her stepping up and admitting what had happened, making the announcement, reflects who she is and the integrity that she carries," Simon said. " . . . I mean, she has made no excuses, none at all, it was all on her, and I think that says a lot.''
While Sharapova awaits her punishment, Williams is gearing up for her first competitive action in weeks.
After getting upset in the final at the Australian Open, she pulled out of tournaments in Qatar and Dubai because of the flu. She returns to the court here Friday night. She said her game right now is "OK. I'm always a little nervous coming into any tournament, but it's all right, hopefully."
Williams said she would like to stick to a vegan diet but hasn't been able to because "I couldn't quite give up the chicken. And then the tacos kind of creeped back into my life. But I don't eat red meat and a lot of other stuff, and so I was educating myself through Venus on a lot of things to remain healthy."
Still, she did go vegan during the 2013 French Open, which she won. "I wasn't tired. It was good. It was really good. I don't know why I don't do that more often. Maybe this year I need to get back on that."