New owner Tony Fernandes signalled his interest in bringing the 36-year-old former Manchester United midfielder to the club on Twitter this week.
And Warnock was quoted in the Daily Telegraph as saying: "About three weeks ago I would not have dreamed to sign Joey Barton so I will never write anything off.
"The chairman Tony Fernandes has got such [an opinion] - why accept the average when you can reach for the top? That is how he is.
"It came out of the blue. I think anything is possible. He is a very astute businessman."
Beckham is in the final year of his Major League Soccer contract with the Los Angeles Galaxy.