Kylian Mbappe is planning to sign a pre-contract agreement with Real Madrid in January after Paris Saint-Germain failed to reply to the Spanish club's £154.4m (€180m) offer.
Real made a second improved bid of £145.8m (€170m) plus £8.57m (€10m) in add-ons and set PSG a deadline to respond by 5pm UK time.
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However, no response was forthcoming, meaning Real are likely to wait until January when they can sign Mbappe on a pre-contract agreement for him to join for free next summer.
The French forward reiterated to PSG on Monday that he will not renew his contract, which expires at the end of the season, as he wants to move to Real.
PSG are still keen to convince Mbappe to sign a new deal, but it is understood there is now no chance of the 22-year-old agreeing to do so.
Mbappe turned up to France's Clairefontaine headquarters on Monday as the world champions prepare to face Bosnia and Herzegovina, Ukraine and Finland in their upcoming World Cup qualifiers.
Mbappe scored twice for PSG on Sunday evening as they won 2-0 at Reims. He said on social media after the game it was "the perfect night".
PSG sporting director Leonardo said last week Mbappe wanted to leave but they would not sell him in the final week of the window and they would not sell him for less than his market value.
Analysis: Could Real go back for Mbappe?
Sky Sports News' Kaveh Solhekol on The Transfer Show:
"There is still a chance Real could increase their offer. I've been told PSG will find it difficult to turn down a bid of €200m. So in the next few hours, could Real go back in and increase their offer?
"What I'm being told is that Real Madrid may go back in - maybe. I don't think they will, I was told they won't go back, but obviously the clock is ticking, the deadline is tomorrow. I think they will consider it and there is still a chance they will go back with an improved offer. There is also still a chance PSG will accept the offer that is already on the table.
"But the official line is that at the moment, PSG will not accept the offer at the moment and Real Madrid will not increase the offer.
"Real Madrid's position now is this - the deadline they set has passed, they're now going to walk away because they are sure that they will get Mbappe next summer for nothing. If that's what PSG want, to kiss goodbye to €180m, that is their decision.
"Real Madrid have tried to conduct themselves properly by paying what they believe the player is worth, despite having 10 months left on his contract, and PSG have basically ignored them.
"As far as the player is concerned, he wants to go to Madrid. He will not sign a new contract at PSG, but as things stand, PSG have decided not to respond to the offer and to keep Mbappe.
"In the short term, they will keep him. But in the long term, he will be a Real Madrid player."
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