I got the impression that these rumors are being spread by representatives of PSG to put pressure on Mbappe (but it’s not clear due to what - the reaction of the fans maybe?). There is no confirmation of these negotiations, and judging by the fact that PSG once again announced the desired amount that they want to receive for Mbappe (250 million), this sounds like an invitation to all interested clubs (in fact, only to Real Madrid, but Real Madrid is not interested in such nonsense).
This may be a strategy of PSG management. They may be spreading rumors that Mbappe is interested in renewing his contract with PSG. And as a result, teams like Real Madrid who are ready to bring Mbappe into the squad can offer a bigger sum. And I've also heard rumors that Real Madrid management will try one more time to sign Mbappe before the transfer window closes. But it is not sure yet.
Most of Mbappe's relationship rumors are false. In the last few seasons we have seen Mbappe express interest in coming to Madrid. But every year he renewed his contract with PSG. And it won't be surprising if we see the same thing again.
If I remember correctly, Mbappe only renewed his contract with PSG once and that was last year when he chose between PSG and Real Madrid. He has already realized his mistake and is now trying to escape from there.
I'm sure Real Madrid will try to get him (although Ancelotti recently once again spoke on the topic that Real have a definitive squad and they don't need reinforcements), but this will clearly not be the amount that PSG wants.