The European champions reached an agreement to sign full-back Theo from city rivals Atletico on a six-year deal last week, a transfer reportedly worth €26million.
Saul, meanwhile, has chosen a different path, signing a renewal that ties him to Diego Simeone's side until 2026.
The Spain midfielder is not bitter about Theo's choice, as long as the 19-year-old, who never made a competitive Atletico appearance, respects his former club.
"It is Theo's decision and he will know what he is doing," Saul told reporters at an event to mark his renewal.
"He is a player who came out of our academy and he has to have respect for where he came from and if he does indeed respect us all that I don't mind where he goes.
"If he doesn't want to be here with us then we are not going to keep him.
"We will give all our affection to those who do want to be here and those who don't want to be with us don't matter to us."