I think this deal will be for another time but not for this transfer window. The likely hoof of it happening is very slim, so Real Madrid have to face the reality and move on to sign another player. Mbappe wants to stay at PSG for at least one more season and PSG don’t want his contract to expire before renewing it. This is why Real Madrid is hopeful that they can sign him this season. Sooner or later before the transfer window closes, the fate of Mbappe and that of Real Madrid would have already been decided by then.
Well, it won't be long before full clarity is made. It seems that Florentino Perez held a meeting with the Emir of Qatar Tamim bin Hamad al Thani on June 21 and agreed on a transfer for 200 million plus a bonus of 50 million if Mbappe wins the Golden Ball. If this is all true, then this is already the highest level of negotiations after which the parties will not be able to back down, so as not to lose face. And the official date of the player's presentation already seems to be set for July 23.