Rudiger will join Real Madrid when his Chelsea contract expires this month.
The 29-year-old is currently on international duty with the German national team at the ongoing UEFA Nations League.
“Yes, it is pressure, but it is the history of Real Madrid. They are used to winning and the mentality is that: to win. But their winning mentality goes with my character,” Rudiger told Marca.
“Leadership is something that comes naturally. As a defender, you have to make yourself feel present and talk to your teammates.
“That is what I try to do. I like to have good communication and motivation. I think it’s something that comes naturally to me. It’s not an act. It just comes out like that,” he added.