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.
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.
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.
