Beckham is available on a free transfer as his contract with MLS side Los Angeles Galaxy is set to expire.
The Daily Mail reports that Beckham has been offered an 18-month contract worth a stunning £11.6million by the French side.
PSG president Nasser al-Khelaifi is keen to bring in Beckham in a move to turn the French giants into a European football superpower.
PSG’s Qatari owners are confident Beckham will sign a deal to join the Ligue 1 leaders in January.