After being challenged on Twitter to take on the 16-time grand slam winner, Murray revealed he was interested in taking part in such an exhibition.
The mere suggestion that the pair could play each other has echoes of the time the then 55-year-old Bobby Riggs, a tennis superstar of the 1930s and 1940s, took on Margaret Court and Billie Jean King.
Those matches in 1973 drew huge worldwide attention, particularly the latter, in Houston, that was dubbed the Battle of the Sexes.
Riggs overcame Court but was beaten by King, with their match the central act in a new documentary film, while Jimmy Connors defeated Martina Navratilova in Las Vegas in 1992.
Six years later, Williams was herself involved in a well-known encounter, taking on Karsten Braasch, then ranked 203rd in the world on the men's tour, during the Australian Open.
Williams reckons she would still lose to the German, even though he is now 45, and would be open to facing Murray.
"He's challenged me? Really? He wants to play me? Is he sure?" she said with a laugh.
"That would be fun. I doubt I'd win a point, but that would be fun.
"[I've done it before but] I was really young. I'm a lot more experienced now.
"He's probably one of the top three people I definitely don't want to play.
"But, yeah, maybe we can have a little bit of a showdown. That would be fine.
"I get alleys (tramlines). He gets no serves. I get alleys on my serves, too. He gets no legs."
Williams later adjusted her expectations of the match upwards, saying: "Maybe I can get a game. I'm not sure, but I think I can get a game."
Murray had earlier written in his BBC Sport column: "I'd be up for it, why not?
"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.
"It's happened in the past with Jimmy Connors and Martina Navratilova. How about Las Vegas as a venue?"
Williams would rather not play on American hard courts, but an indoor venue in the US gambling resort could be an option.
"Indoor, grass, I'm going to have to choose grass indoor," Williams said, speaking after her second-round win against Caroline Garcia at Wimbledon.
"Actually, I might go clay. I think I might go clay with him. He loves grass. I do, too. But I'm going to definitely go clay."