The goalkeeper left PSG for Real last week on a season-long loan.
Lloris said, "Of course we exchanged. What we said remains between us. We must take the thing very positively, he will join the most prestigious club in the world.
"For it to be positive, it must be taken in a positive way. You never know what will happen, you have to be ready for any eventuality.
"After (Gigi) Buffon, he will share his daily life with (Thibaut) Courtois. We know the expectations at Real Madrid, we must always respond and he will certainly have the chance to evolve under his new colors."