reporter Kaveh Solhekol revealed Real were willing to pay more than £188.9m for Mbappe.
The journalist claimed the move was 'completely' off for the time being and the Spanish club would try and sign the 22-year-old at a later date.
Solhekol's report was immediately shared across social media, allowing a PSG boss to write a response to his 150,000 Twitter followers.
Khalifa bin Hamad Al Thani, a member of the family that own the French club, wrote: "€220m. Now you can call. The line is open."
Rumours suggest PSG stalled on the attractive offer and Real will now attempt to get the World Cup winner for FREE next summer.
The LaLiga side can sign Mbappe on a pre-contract agreement in January ahead of his existing PSG deal expiring in June.
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Players can open negotiations with foreign clubs when they enter the final six months of their contract.
If Mbappe doesn't complete a move to Real before the end of the current window, PSG will have another four months to persuade him to stay.
The club's sporting director Leonardo, who has criticised Real's pursuit of the player, recently said: "PSG's position has always been to keep Kylian.
"That's been the aim for the last two years and it remains unchanged... and we are not going to sell a player for less than we paid for him."
PSG are hoping the prospect of playing with superstars Lionel Messi and Neymar will encourage Mbappe to sign a new deal.
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Kylian Mbappe shows off his football skills at PSG training