Valverde was grown up by Real Madrid and he is one of their best young midfielders. Casemiro was sold, Modric is too old and likely will have last one to two seasons with Real Madrid, Kroos is already old enough and Valverde is one of best midfielders for Real Madrid future. He loves the club, play well and Real Madrid will send him to another club. Except if Real Madrid buy a very expensive midfielder and Valverde loses his position in the squad then will feel unhappy, a transfer might occur.
So far, no signal for such things in Real Madrid and he will stay in the club. Real Madrid will not sell him just to buy Mbappe in my opinion.
The story with Mbappe should be decided soon, PSG president Nasser Al-Khelaifi said that Mbappe has two weeks to decide on his future. PSG are not going to let one of the most expensive players in the world go for free, so they gave him two weeks to either continue his contract with the club or be sold in this transfer market. I don’t know if it makes sense for Real Madrid to shell out such a lot of money for Mbappe, yes he is an excellent forward, but is he really worth that much money?