PSG are candidates to acquire the 80,000-capacity, government-owned national stadium situated in Saint-Denis, just to the north of Paris itself, after a first deadline for potential buyers to come forward passed on Thursday afternoon.
The new owners would take over when the current lease on the stadium, which will be the centrepiece of next year's Paris Olympics, expires in July 2025.
The price of the Stade de France, which was built for the 1998 World Cup finals, was estimated at 647 million euros ($712m) by the French government in 2021.
The Stade de France is the home of the French national football and rugby teams and is due to host the final of this year's Rugby World Cup in October.
French press reports have indicated that both FIFA and UEFA are also interested in buying the stadium, yet world football's governing body has denied doing so and UEFA has not commented.
It is understood that whoever acquires the stadium will need to carry out significant refurbishment work.
Should PSG become the owner, their plans would include bringing the stands closer to the pitch -- they are currently separated by a running track -- and reducing the capacity to 70,000, according to a club source.
However, PSG appear to be looking at the stadium as a back-up option because negotiations with Paris City Hall over the Parc des Princes have so far not proved fruitful.
They have played at the stadium, situated in the city's upmarket 16th arrondissement and with a capacity of around 47,000, since 1973.
A club source told AFP that buying the Parc des Princes remained PSG's "plan number one, two and three, and buying the Stade de France is number four".
The other possibility is building a new stadium, perhaps at the Saint-Cloud racecourse just outside Paris or further out of the capital at Poissy, where the club is currently building a new training centre.
PSG have said they want to expand and renovate the Parc des Princes, bringing the capacity up to 58,000 at an estimated cost of some 500 million euros.
In the eyes of the club's Qatari owners, Qatar Sports Investments, that work could only be made possible if PSG became the owners of the stadium.
"We opened the door to the possibility of selling the stadium to our club because it is true that if you look at the economic model of the biggest clubs, almost all of them own their stadiums," Paris mayor Anne Hidalgo told radio station RFI on Thursday.
However, she added: "There are also prices that must be set and must correspond to the property in question."
She said that the club had offered 38 million euros to buy the stadium, a figure she described as "ridiculous".
Despite that, Hidalgo also said she thought PSG would not end up leaving.
The authorities have said they are open to finding other solutions but PSG affirm that they will only return to the negotiating table if it is to discuss buying the stadium, which remains their "priority".
"Like all clubs on the European scene, we need to own our stadium," the club source said.
That will reassure PSG supporters who do not want to move.
A banner that has been put up near the stadium reads: "PSG was born in Saint-Germain, grew up at the Parc des Princes, died under QSI and will be buried at the Stade de France".
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