PSG - flush with cash after the arrival of new Qatari owners in the summer - have become the favourites to sign Beckham after the 36-year-old revealed he has been courted by "two big European clubs" after helping the Galaxy to the MLS title last weekend.
And PSG's sporting director Leonardo said earlier this week he had been in touch with the former Manchester United and Real Madrid star, whose contract with Los Angeles Galaxy runs out at the end of December.
According to the Mail, Beckham is considering an offer from PSG for an 18-month contract worth a £11.6million (15 million euros) with PSG president Nasser al-Khelaifi seeing him as the star turn to help turn the club into a top name.
PSG are desperate to land their first league title since 1994 and beyond that ramp up their profile worldwide.
Helping their cause, former AC Milan manager Leonardo already has a good relationship with Beckham having coached him during his loan move at the San Siro last year.
"If Beckham thinks about coming, that's something we should be happy about," Leonardo said quoted in The Sun newspaper earlier this week.
"I think he can still bring something on the pitch with the person he is and the experience he has."