The 33-year-old England midfielder is on loan at Milan until March 9 but has said he wants to stay with the Serie A team permanently.
"We made an offer to Galaxy which they have not accepted," Galliani told Sky television at Milan's home league game with Reggina.
"For now we are a long way apart but there is still a month to go," he added without going into details about the offer.
For technical reasons Beckham's loan is actually until June, meaning Milan can talk to Galaxy outside of the transfer window which closed last Monday.
However, there is a written agreement that he goes back to the U.S. in March.
The Galaxy have said Beckham will return to Los Angeles as scheduled unless Milan come up with a substantially higher offer.
"If David ultimately is an asset for this team, we want him back," Tim Leiweke, chief executive of AEG, the entertainment conglomerate that owns the Galaxy, told the Los Angeles Times on Saturday.
"If David ultimately has a hunger and a desire to come help us make the impact on the pitch that we wanted to make with him but haven't done yet, then he's an important member of this team and our intention is to bring him back.
GALAXY COMPENSATION
"Clearly, if David's in a position where he wants to finish the season in Milan and Milan in turn compensates the Galaxy so that we can suffer no damages to our fans or to our team, then we'll take a look at it.
"But we have made it very clear to them that we expect David back here March 9. They agree and understand we own the contract. They understand the only way we do this is if, when this is all said and done, the Galaxy benefits.
"If the Galaxy comes out better without David than with David, then we'll take a look at it."
Former England captain Beckham joined the Galaxy in 2007 on a five-year deal as part of an orchestrated bid to lift American soccer to a new level.
Two unsuccessful seasons later, however, he has set his sights on a permanent move to Italy to help him play one more World Cup with England in South Africa next year.
After scoring just five goals for the Galaxy in 30 games since his arrival in Major League Soccer (MLS), Beckham has remembered what it is like to play soccer in the top flight.
"We understand his infatuation with playing on (one of) the world's most popular club teams and we understand his trying to mentally get around the idea of coming back to play with a team that didn't make the playoffs in MLS last year," Leiweke said.
"That said, David and us actually are talking. He has never forced our hand on anything. David has made it very clear that if our decision is to bring him back here, he will return. Period."
