The 33-year-old Beckham has been playing for the Galaxy in Major League Soccer in the United States, but his contract expires in March.
He has scored twice in five games since his arrival from the Galaxy, and wants to make it permanent.
"At the moment, my lawyers are not talking to the Galaxy but I have expressed my desire to stay at AC Milan now and it's just down to Milan and Galaxy to come to an agreement," Beckham said after Milan's match (friendly) on Wednesday. "I knew I would enjoy it but I didn't expect to enjoy it as much as I have and do as well as I have. I've expressed my desire to stay with Milan but it's out of my hands."