It seems that Real Madrid prefers the option of waiting until Mbappe contract expires with PSG then they can recruit him for free next season. As you can see, Real Madrid prefers to remain silent rather than make an official offer to sign Mbappe. Real Madrid cool attitude has led to various kinds of speculation to the public, even though they really need a quality striker to replace Benzema role.
Real Madrid weakness is in the striker position, so far they have just brought in Joselu who is 33 years old, based on his age, he is not the main one in Ancelotti squad. Based on the needs of clubs on every front, Real Madrid really needs a quality striker to increase their attack power.
If they intend to sign Mbappe as a free agent then it will come with a cost. PSG said Mbappe must sign a new contract or leave the club. If he insists he wants to stay till next season, the club said they are ready to keep him on the bench for the entire season. He might even be banned from training with the main team which might affect his performance. The price is that the French striker will be willing to stay on the bench and PSG will also be willing to waste money on his wages. The decision to attract Mbappe to Real Madrid next season might not be coach Ancelotti's decision because he will be leaving the club for a new role with the Brazil national team after the end of this season.
From Real Madrid's last game against Barcelona, it was glaring that without a natural striker in the team, the club might find it difficult to maximize goal-scoring chances. They missed so many opportunities in the game because they lacked a natural number nine. The game against Juventus also proved the need to get a striker where they had thirty-four shots, eight on target, and scored just one goal after having total domination of the game. If Mbappe is too expensive, the club should seek cheaper options.