“He wants to play me? That would be fun,” Williams said after sweeping past French teenager Caroline Garcia 6-3 6-2 in round two at Wimbledon on Thursday.
“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.”
Should an exhibition game between the Murray and Williams happen, it would be a match between the two 2012 Olympic gold medal singles winners.
While Murray defeated Roger Federer to clinch the men’s title at the Games, Williams overcame Maria Sharapova to win the women’s event.
When the idea was put to world number one Novak Djokovic, the Serb said it would be “a lot of fun to watch”.