who were taken over by Qatar Sports Investments (QSI) more than a decade ago.
QSI, a subsidiary of the Qatar Investment Authority, the Gulf state's sovereign wealth fund, gained control of the French club in 2011 for just 70 million euros ($74.7m at the current exchange rate).
PSG have since become a vehicle through which Qatar can project soft power – under QSI's ownership, they are now not just France's dominant club but a leading name on the European stage and a global brand.
More than 1.5 billion euros has been splashed on transfers over the last dozen years, including the two biggest fees in the history of the game for Neymar and Kylian Mbappe in 2017, although all that money has not yet delivered Champions League glory in which Qatar could bask.
But now the tiny, gas-rich state is aiming even higher with its sights set on United, the most successful club in the history of the most powerful league in the world, with commercial and broadcasting income far greater than what can be generated in the French top flight.
The bid, led by the chairman of the Qatar Islamic Bank (QIB), Sheikh Jassim Bin Hamad Al Thani, is believed to be worth between four and six billion euros, according to several sources.
The QIB is owned by Qatar's sovereign wealth fund.
"When you have an offer from someone who is a member of the wider Al-Thani family, it inevitably means it is an offer from the state," Jean-Baptiste Guegan, a lecturer and specialist in geopolitics in sport, told AFP.
"This means nothing has been done without the approval of the emir, Sheikh Tamim bin Hamad Al-Thani."
However, there is no suggestion of the Qataris abandoning PSG in the short or medium term.
NEW STRATEGY?
If the Qatari bid for Manchester United succeeds, "the plans for PSG would not change at all. The two clubs would be totally separate on the field and off it. The QIB is totally separate from QSI," a source close to PSG's owners insisted to AFP.
Last December, PSG president Nasser al-Khelaifi also shut down any suggestion of a possible withdrawal when he said in an interview with the Financial Times "we have a long-term project here".
At the same time, Khelaifi admitted the French champions had been in discussions with several investors about potentially selling a 15 per cent stake.
"Qatar is capable of persisting with the two clubs. That doesn't mean that it is finished with PSG. It is above all a demonstration of Qatar's power that it is able to show an interest in a club like Manchester United," Raphael Le Magoariec, who specialises in the Gulf and sport at Tours University in France, told AFP.
"It is unlikely that they would withdraw from Paris because that would be seen as a failure."
Nevertheless the dispute with Paris city council over PSG's attempts to buy their Parc des Princes stadium from the local authority has left a bitter taste with the club's owners.
Qatar, according to Le Magoariec, "has invested a lot and thinks that its generosity is not being respected".
Despite that, the ties between France and Qatar, which possesses stakes in numerous French multinational corporations, make it unlikely the country will divert its capital away from a club like PSG.
"Paris is the type of platform which gives Qatar standing in the world," says Le Magoariec.
Yet it is possible a slight change in strategy at PSG is taking place, given the club is being closely watched by Uefa to ensure they fall in line with the Financial Fair Play (FFP) rules of European football's governing body.
The club made huge losses last season of 370 million euros and has an enormous wage bill, weighed down by the salaries of superstars Mbappe, Lionel Messi and Neymar.
"There is maybe less investment. They have already tightened their belts because of FFP constraints," said Guegan.
"But they are going to open up to foreign investors, and depending on the identity of these investors we will see if the club continues to be an asset in Qatar's strategy of visibility or if they move on to a different stage."