The former England captain may opt to remain in the United States for family reasons, with the MLS side keen to re-sign the 36-year-old on a one-year rolling contracthere.
Paris Saint-Germain sporting director Leonardo has revealed that David Beckham may not sign with the Ligue 1 side, with the midfielder potentially opting to stay with current club LA Galaxy, according to the BBC.
It had been widely suggested that Beckham would be interested in returning to Europe once his current five-year deal with the MLS side expires on Saturday.
However, Beckham's reluctance to leave Los Angeles, where he has raised four children since moving from Real Madrid in 2007, could mean the player remains in the United States.
Also, Beckham and his advisors have been impressed with Galaxy's determination to re-sign their marquee player with an offer of a one-year rolling deal.
Beckham, who began his career with Manchester United before moving to Real Madrid, won the 2011 MLS Cup at the Home Depot Centre with LA Galaxy against Houston Dynamo in November.