"David is focused on the Milan derby this Sunday. We will be addressing this early next week," said Beckham's spokesman Simon Oliveira.
BBC Sport understands that Beckham's advisors remain confident that a deal can be brokered next week despite the passing of Galaxy's arbitrary deadline.
Beckham has the option of buying out his contract and has a clause which means he can leave Galaxy for nothing in November, though returning to America for the remainder of the current season could put his place in England's squad in jeopardy.
Beckham had moved to Milan on loan in an attempt to revive his international career after England head coach Fabio Capello said he needed to be playing more competitive football.
The England international, who equalled Bobby Moore's England record of 108 caps for an outfield player in Wednesday's 2-0 defeat by Spain in Seville, has become a regular for Milan since his arrival in January.
However, with England set for nine internationals from the end of March until October, including six qualifiers for the 2010 World Cup, a return to the MLS could see Beckham left out of the national squad.
Milan, who have had a £5m bid for the 33-year-old rejected, have so far failed to meet the Galaxy's valuation, which is reportedly in excess of £10m.
I've been as courteous and as gracious as I possibly can out of respect for David, but now it's time to move on
Tim Leiweke chief executive of AEG
The former Manchester United and Real Madrid star has settled in quickly at the San Siro, impressing both Ancelotti, his team-mates and rival managers with his professionalism and work ethic.
Speaking ahead of the Milan derby, outspoken Inter Milan coach Jose Mourinho said: "Beckham is a great champion and he is trying to remain with Milan.
"For the good of the league, for Italian football, I hope he stays - he has improved Milan as I knew he would when he arrived in Italy.
"The fears people had over his signing were not fair on the player. He is a top professional, has ambition, is in great condition and is always motivated to play well.
"You cannot always control how a player adapts to his new surroundings, but Beckham has clearly adapted to his club and the Italian league.
"He gives his team different qualities and that is a good thing."
Beckham has made a big impact on the pitch, scoring on his third appearance and netting with a trademark free-kick in the recent win over Genoa, a game watched by Capello.
But the chief executive of Galaxy owners AEG, Tim Leiweke, insisted Beckham would have to return to the MLS.
Beckham has been a big hit in Milan - especially with his team-mates
Asked what would happen should the Italian return with an improved offer, Leiweke said the club "owe it to our fans" not to consider it.
Leiweke insists the Rossoneri have never come close to meeting AEG's and the league's asking price.
However, US football expert Sean Wheelock told BBC Radio 5 Live that he thought Beckham could still end up at Milan.
"Until I actually see a definite statement coming out of the New York offices of MLS soccer and quotes of the league commissioner, Don Garber, I don't believe that this matter is resolved," said Wheelock.
"I still think that there is a chance - albeit a slim one - that David Beckham could stay permanently at AC Milan and may not return to LA Galaxy. I just don't think this is a resolved matter."
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