A deal between Mbappe and Real Madrid is being discussed a lot but so far nothing can be said for sure whether Real Madrid will finally sign Mbappe. The summer transfer market won't be open for long so it's probably during this period that Real Madrid will decide on the next player they sign for their squad.
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.