Club chairman Tony Fernandes revealed earlier this week that he is interested in the player, while the manager admits he will "never write anything off" under the new owner
Beckham's contract at LA Galaxy expires in November and it is anticipated that he will not renew his deal, with a return to England on the cards.
Earlier this week QPR owner, Tony Fernandes confirmed his interest in Beckham via Twitter, hinting that a deal may be on the horizon.
And when asked about a potential move Warnock told The Telegraph: "About three weeks ago I would not have dreamed to sign Joey Barton so I will never write anything off.
"The chairman 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 has kept himself busy through the winter months when the Galaxy are not playing, spending two spells with AC Milan and last season training with Tottenham before a loan move broke down.