British number one Murray suggested that the duo play each other in Las Vegas to see how their styles compare, and the American has risen to the challenge.
"I'd be up for it, why not?" the Scot wrote. "I've never hit with her, but she's obviously an incredible player and I think people would be interested to see the men play against the women to see how the styles match up."
Williams responded by saying that she would happily take on Murray providing it was on a clay surface, rather than grass.
"That would be fun. He's probably one of the top three people I definitely don't want to play," she replied.
"But, yeah, maybe we can have a little bit of a showdown, on clay. He loves grass. I do, too. But I'm going to definitely go clay.
"That would be fine. I get to use the doubles alleys, he gets no serves. And he gets no legs. If we agree all that, then maybe I could get a game off him. I'm not sure, but I think I could get a game, fingers crossed."