Both Murray and Williams are fully focused on their respective Wimbledon challenges, but the Brit has been questioned as to whether he would be able to beat Williams on grass.
The prospect of a clash has revived memories of the matches in the 1970s when a 53-year-old Bobby Riggs, a star of the 1930s and 1940s, took on Margaret Court and Billie Jean King.
Those matches in 1973 drew widespread attention and when King faced and beat Riggs, it was known as the Battle of the Sexes.
Murray replied to the Twitter user that he would probably be beaten by Williams on grass, but it has not put him off issuing a challenge.
He wrote in his BBC Sport column: "I have been challenged by someone on Twitter to taking on Serena Williams. 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?"
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