"Beckham's lawyers are talking to the Los Angeles Galaxy who still legally own his rights," Galliani is quoted as saying on the Milan's website.
"If they are willing to negotiate then we will be very happy to discuss the situation. We are neither optimistic nor pessimistic right now.
"Beckham is a Galaxy player and we hope that they will decide to sell him.
"We will try to sign David on loan until the end of the season or even permanently. We will be very disappointed if he has to leave.
"The Galaxy have been very polite in their dealings with us. We haven't made any official offer. The lawyers are dealing with it and they have until March 8 to seal a deal."