The offer, reportedly worth €65 million, was made in the last 24 hours after Heung-min Son's transfer to LAFC.
Rodrygo was initially hesitant to join Tottenham due to the club's reputation, despite its recent Europa League success.
However, the player's stance may have changed in recent weeks, possibly due to the lack of more attractive offers from other top European clubs.
Tottenham have requested permission from Real Madrid to negotiate directly with Rodrygo, indicating a serious interest in signing him.
