French media said Beckham turned down a lucrative offer to join Paris St. Germain after five years in Los Angeles. Galaxy owners said they had not yet reached an agreement on a new deal.
"We've been talking for four months, we continue to talk to David and we think we are making progress," AEG Enterprises President and Chief Executive Officer Tim Leiweke told the Los Angeles Daily News. "We are intent on getting a deal done to keep David here."
Beckham arrived in Los Angeles to great acclaim, with expectations his presence would boost interest in the Major Soccer League. The Galaxy won the league championship this season.
Beckham, 36, is considering a one-year deal with the Galaxy and has also received interest from Britain's Tottenham Hotspurs Premier League side, the newspaper said. Any new MSL contract would have to be approved by the league and would likely include an ownership share of the Galaxy.
The Galaxy will open training camp this month, with players reporting for physicals Jan. 18.
Notable deaths of 2014 [PHOTOS]