The British number one sent a tongue-in-cheek message to a fan on Twitter in response to the suggestion that Williams could beat him on grass.
Last summer the American, 31, won Wimbledon and double Olympic gold at the All England Club.
Twitter user Tom Carswell wrote: "I recon (sic) serena williams could beat u on grass..And I'm not even joking."
The Scot responded: "me too! Maybe we can set it up one day and see how close I get".
Murray has taken to Twitter on several occasions during this year's Championships to update his fans and thank supporters for their encouragement.
"Good to get through today, always a lot of nerves before the first match," he wrote after his opening clash.
"Was nice to be back on centre court thanks for the support again!"
In another posting, he detailed his evening routine: "Post match chores.. Shower..10min bike..sushi..45 min physic..1hr press..10 min ice bath..5min warm bath..now mock the week in bed!"