Los Angeles Galaxy have continually said the 33-year-old England midfielder must return to the United States on Monday once his two-month loan deal ends, but Milan still hope to persuade them to let Beckham stay in Italy until June.
Milan had tried to buy him outright but a disagreement over price means frantic negotiations are now taking place to simply extend the loan, with the hope that Beckham could then move full time to Italy at a later date.
An announcement could come on Friday but so far Galaxy have stuck to their guns.
"I have no news but obviously I still hope to stay," Beckham told reporters.
He had a bright start to his Milan career but his performances have dropped slightly of late as his third-placed side slipped 12 points behinds leaders Inter Milan and virtually out of the title race.
Last weekend's 2-1 defeat at Sampdoria was a big blow to coach Carlo Ancelotti, who has been told that anything less than a third-placed finish this season and automatic entry into the Champions League could leave his job on the line.
A win over Atalanta therefore becomes paramount but playmaker Kaka is again likely to miss out with a foot problem.
Champions League second legs against Manchester United, Chelsea and Arsenal next week mean Inter, Juventus and AS Roma play on Saturday in a series of intriguing games.
A much-changed Inter were beaten 3-0 by Sampdoria in Wednesday's Italian Cup semi-final first leg but their best side are expected to visit fifth-placed Genoa, who have not lost at home in the league this term.
Juve, seven behind Inter in second, must negotiate a derby with Torino and Roma coach Luciano Spalletti hosts former side Udinese.
