Inside sources at the Parisian club told French sports daily L'Equipe that Beckham's PSG move was "95 per cent complete."
If confirmed, it would spell an end to the British icon's five-year stay in American soccer. He led the L.A. Galaxy to the 2011 MLS Cup and was given best 11 honors for his performances over the course of the season.
His 2007 signing was a boon to MLS off the field, but it de-stabilized the club on it. Loan moves to AC Milan in 2009 and 2010 were attempts at prolonging his international career, but they caused rifts with Galaxy teammates and management, who questioned his commitment to the club.
An achilles injury he suffered with Milan cost him most of the 2010 season, but Beckham regained his fitness and became a key figure in the Gaxy midfield.
PSG is looking to become one of the giants of world soccer. The ownership of the the Qatar Investment Authority (QSI), which bought a 70 percent stake in the club in May has seen it spend £72.9 million ($114.5 million) on new players in the last six months.
Beckham's addition would further raise its profile on the world stage, but analysts question the potential on-field impact he would have. After 17 games the capital club is second place in France's Ligue 1, trailing HSC Montpellier on goal difference.
The 36-year-old's contract with Los Angeles expires on Dec. 31, and he has not announced if he intends to stay in MLS.
