Valverde is still very much needed by Real Madrid so an offer that is not too high will certainly be rejected by Real Madrid. And right now Liverpool are in need of a midfielder. because there are already around 3 Liverpool midfielder players who left Liverpool in this transfer market. And now Liverpool have got 2 new midfielders. and of course Liverpool still need 1 additional midfielder again. And it is possible that Liverpool will return with a higher offer for Valverde.
Valverde is one of players who were bought as future preparation for Real Madrid. In last several seasons, he is one of most fastest growing players together with two Brazilian players Vinicius and Rodrygo. Real Madrid will not sell Valverde when they need him and both are happy with each other. Valverde did not say any word that he is not happy in Madrid and want to leave the club.
The offer from Liverpool is not big enough to bring Valverde out of Bernabeu too. Real Madrid is not a club that is ready to sell their star players when they are young and usable for the club. Especially with Valverde, we know he is happy with his club, not like Nikolas Anelka in the past.
Every team will want to sign Valverde and have him play for them, but for the time being Real Madrid won't allow him to leave because he is one of their best players and will perform well in the upcoming season no matter what is going on or how much more money is offered. This is due to Real Madrid's policy of never trading away a star player, especially one who is still proficient in his position.
I'm assuming that there are some teams, like Liverpool, Barcelona, and Chelsea, that are constantly on the lookout for good players and are willing to pay whatever price is necessary to acquire them. These teams want to ensure that they have all the ideal players in their lineup for the upcoming season.