the reason Valverde will stay is that Madrid have yet to get a replacement in his position. so there is no reason for Valverde to leave Madrid. even though there were big offers from Arab clubs, even from Liverpool who also wanted to sign him.
we don't know how ambitious Madrid will be to sign Mbappe, if it actually happens. Maybe Valverde will indeed be released to Liverpool. some rumors of the talk are already in the media. so we're just waiting for the truth.
it is very unlikely that Real Madrid will have to replace Valverde with a new player because Valverde is a reliable player in the central midfield position and all that was proven when Madrid extended his contract until 2027. we probably won't know what will happen in the coming season but usually Real Madrid will not let go of players who are still very young like Valverde.
Even if Real Madrid is too ambitious to get Mbappe, that doesn't mean that they have to sell their midfielders or if they don't choose to sell old players it makes sense.