The Brazilian is regarded highly by new Real coach Jose Mourinho.
"I am comfortable with these things but impressed. Madrid and Benfica are among the best clubs in the world. I try to keep in mind that we must live each day, you cannot live the dream if you don't work every day with devotion. Recognition, of course, makes me feel proud," he told AS.
"Real is the name in the mouths of children around the world. It is the top, the best institution in history without a doubt, a club whose shirt is steeped in history and all players want to wear it.
"Look at Kaka and Cristiano [Ronaldo], which are the best players in the world and they have this hunger and this will to wear the white shirt."
Luiz also stated that if there is a deal on the table which suits all parties, he would be unable to refuse.
"If that's best for Benfica, the best for everyone and the president understood well, why not? I'm proud to see my name linked to Madrid. Who could say no?"