The 32-year-old winger's contract will expire this summer, and plenty of top European clubs are interested in signing him, being one of the most highly rated wingers in Europe.
The Ligue 1 side are hoping to get him to sign a new contract at the club, after repeated failed negotiations over a new deal last year.
However, Spurs are keen on Di Maria according to L'Equipe, with a possible move seeing him reunited with his former Real Madrid manager Jose Mourinho, with the London club making the first contact with the winger.
Di Maria had previously rejected PSG's new contract offer mainly because they were proposing a wage cut to his current wage of £220,000 per week.
Apart from this, Di Maria was also keen on a two-year deal to try and finish his career in France, however PSG were reportedly set to offer just a one-year deal.
Additionally, Juventus are also said to be interested in Di Maria, but Spurs are the front runners for the deal.
Di Maria has repeatedly praised Spurs manager Mourinho throughout his career, telling Diario Ole in 2013 that "Mourinho made me a better player" and that "He showed me many things and made me grow as a footballer. He helped me to move into a different position, to sacrifice myself more for the team."
"I'm very grateful to him. He told me that, at Real, I was a forward that could also defend and that I couldn't rest when they were on the attack."
Di Maria has four goals and ten assists in 22 games in all competitions so far this season, being a regular starter for the Ligue 1 side.
The 32-year-old has played 243 times for PSG, and during that time he has managed 86 goals and provided 102 assists, remarkably winning four Ligue 1 titles, along with four Coupe de France and Coupe de la Ligue titles, as well as four Trophee des Champions.