The 33-year-old soccer hunk – on loan from the LA Galaxy to Italy's AC Milan – has already made clear his desire to continue playing the European circuit.
But on Sunday, Beckham confessed that a return to Los Angeles would be awkward.
"I've said I want to stay here, and if I do go back then it will be a bit difficult, but we'll have to wait and see what happens," Beckham told reporters after his AC Milan team was beaten by local rivals Inter Milan, 2-1.
Asked if he might see the issue resolved over the next few days, Beckham responded: "I don't know. It is out of my hands, and they'll be talking in the next week or two."
Approached by PEOPLE, Beckham's U.K. rep was unavailable for comment.
LA Won't Let GoThe head coach of LA Galaxy, Bruce Arena, made clear last Friday that Beckham is under contract and expected to return to California for the new season.
"Today's deadline imposed by Major League Soccer Commissioner Don Garber regarding a resolution of David Beckham's potential transfer to AC Milan has passed, and we did not receive an acceptable offer for the player," he said.
"As a result, David remains an LA Galaxy player and we look forward to having him back with the club starting March 9."
A source close to the soccer star tells PEOPLE that whichever team gets to keep Beckham, his children will remain in America.
"Whatever happens the boys, Brooklyn, Romeo and Cruz, will stay in Los Angeles," says the source. "There is already a family decision to keep continuity with their education."