New Real coach Carlo Ancelotti is expected to reinstall Iker Casillas as first-choice goalkeeper for the new season.
"In January, when I arrived, I said that it was a dream for me to come back home to this club. I have never thought about leaving," said Lopez.
"I have confidence in my ability and about maintaining my level and improving. If there have been offers then it is up to Real Madrid to evaluate them, but my position has always been to stay. I knew what was coming and I'm ready for the pressure at this club. I live thinking about my training sessions, taking care of myself and being a professional. When you're so into your work, you don’t even hear anything that is going on away from that."