Kylian Mbappe is planning to sign a pre-contract agreement with Real Madrid in January, after Paris Saint-Germain refused to sell him this summer.
PSG failed to respond to Madrid's €180m offer, according to Sky Sports.
The Spanish club made an improved bid of €170m plus €10m in add-ons, but set PSG a deadline to respond by 5pm UK time.
However, with no response forthcoming, 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 22-year-old reiterated to PSG on Monday that he will not renew his contract, which expires at the end of the season.
PSG are still keen to convince the France forward to sign a new deal, but it is understood there is now no chance of him agreeing to do so.
Mbappe has gone away with his national team, to prepare for their upcoming World Cup qualifiers against Bosnia and Herzegovina, Ukraine and Finland.