The problem is that Real Madrid is demanding a high price for Rodrygo and given his performances this year he's been deemed insufficient, so some interested clubs are having to reconsider. Perhaps if the price were lowered slightly, he could leave, whether to Liverpool or Arsenal. Clearly Rodrygo needs to consider this move to get decent playing time and maintain his magical foot potential.
Real Madrid are aware of Rodrgyo quality as well as his transfer price estimation so they won't let this player leaving with a cheap price or as a free agent. They also need to get as much money from his transfer as possible in order to use it for their team rebuilding with other star players. Liverpool, Arsenal, Chelsea, Manchester City or any big club that wants to have Rodrygo will have to pay high cost for this transfer and surely give Rodrgy a kind of lucrative wage offer.
Arsenal and Liverpool are aware that buying a player from Real Madrid doesn't come so cheap, especially if the player is of high profile. Either clubs are willing to pay for Rodrygo if only he agrees. Even AFC is ready to break the bank despite how annoying they can be to releasing money for a player they want.
At the end of the day, he has to make his choice, because the more he keeps sitting on the bench with no playing time, the more his value diminishes. And he is not getting younger anymore too.
Not all players who play for Real Madrid are star or super star players, and your post is just completely wrong. Transfer cost can be cheap or expesive and it depends on the player quality, not the club name like whether it is Real Madrid, Barcelona, Liverpool or a club that usually struggle to stay in a league like Girona.
Rodrygo specifically is one of best star players in this generation and he belongs to a list of star players only behind best ones for Ballon d'Or competition. As a star player with high quality and potentiality like this, Rodrygo certainly has very high transfer price on the transfer market and Liverpool have to pay kind of high cost to buy him from Real Madrid.