Beckham, 37, has announced he will leave the Los Angeles Galaxy after next month's MLS Cup and is looking for one last club with which to bring the curtain down on his career.
PSG, bankrolled by Qatar, made an offer to the player a year ago and the presence of head coach Carlo Ancelotti and sporting director Leonardo, both of whom Beckham knows from his spells at AC Milan, could prove the clincher.
It is understood the French club remains a strong option but there has been interest from all around the world, including wealthy clubs in China, Russia and even Brazil.
Beckham's representatives have dismissed claims from Australian clubs however that they are in talks about a move to the A-League. It is understood that such a move, or to New York Red Bulls, remain the least likely options, while chances of a return to the Premier League in England also appear slim.
Beckham will spend the next month making his decision with his choice likely to be announced in mid-December after the Galaxy's title defence against the Houston Dynamo on December 1 and subsequent tour.
Although Beckham had an option on his contract, signed in January, for a seventh year with the Galaxy, his decision to leave is no great surprise.
He told the Major League Soccer website: "I've had an incredibly special time playing for the LA Galaxy, however, I wanted to experience one last challenge before the end of my playing career.
"I don't see this as the end of my relationship with the league as my ambition is to be part of the ownership structure in the future," Beckham added.
Beckham's stint in Los Angeles brought success in the form of the Galaxy's third MLS Cup crown last year.
But he also faced repeated criticism from some Galaxy fans, particularly early on in his stay, for a perceived lack of commitment to the cause.
Two loan stints at AC Milan, during the second of which he tore an Achilles tendon, as he attempted to keep his place in the England team did little to help that perception, as well as comments made while in Italy about the standard of football in America.
Two low points arrived back in 2009 when Beckham confronted a fan during a match after his every touch was booed and attracted criticism from team-mate Landon Donovan.
Since then he has won over many supporters, in no small part due to a dramatic upturn in form over the last two seasons, and he was voted the league's best player by fans earlier this year.
Beckham was brought to America as much for the effect of his brand as his on-field ability, and MLS commissioner Don Garber believes he has been successful in helping to grow the sport.
"When David Beckham signed with the LA Galaxy in 2007, he set out to help grow MLS and the sport of soccer in North America," he said.
"There is no doubt that MLS is far more popular and important here and abroad than it was when he arrived.
"David has achieved great things on and off the field during his time with the Galaxy, and he will always be an important part of our history. We look forward to his continued involvement with the LA Galaxy and the league."
Beckham's initial contract with the league included a clause allowing him to be involved in owning an expansion team down the line.