The deal will see the England international stay at San Siro until the end of the season.
“The negotiations are progressing,” Milan Vice-President Adriano Galliani confirmed on the Milan Channel.
“I’m hoping we will be able to get Beckham to stay here on loan until June 30.
“Then he would be able to return to Los Angeles and come back here in January. It’s a complicated deal, but we believe in it.”