Real Madrid have offered Paris Saint-Germain 310 million euros for Brazil striker Neymar, according to a report by Televisión Española (TVE) on Monday.
TVE says that Los Blancos are yet to receive a firm response from PSG.
Were such a deal to take place, it would be the most expensive in history, surpassing the 222-million-euro fee paid by the Ligue 1 club to sign Neymar from Barcelona last summer.
TVE adds that Real are preparing to hand the player a seven-year contract worth 45 million euros a season.
The 26-year-old is currently on Brazil duty at the World Cup in Russia, where his 51st-minute goal helped the South Americans to beat Mexico 2-0 in the last 16 on Monday afternoon, setting up a quarter-final clash with Belgium.