The former Tottenham midfielder, who joined los Blancos last season, wants to establish himself at the Santiago Bernabeu, while he also praised former boss Jose Mourinho.
The Croatia international has been linked with a move to Chelsea - and a reunion with recently depart los Blancos boss Jose Mourinho - but has played down speculation surrounding an exit from the Liga runner up.
"I’m not even thinking about the possibility I could leave Madrid this summer, but there is interest from other clubs," Modric told The Sun.
He added, "Every kid who plays football dreams about playing for Real Madrid. It was the same with me. Of course I was sad when Jose Mourinho left. He was the one who insisted in bringing me to Madrid. He is a fantastic coach and I am honored to have worked with him."
Chelsea's new boss will be expected to challenge the Manchester clubs for the Premier League title as well as compete for the Champions League, and Modric believes Mourinho will be a success.
"He really impressed me," he explained. "It’s such a pleasure to play in his team and talk with him about football.I wish him all the best in Chelsea. I believe he will use all his knowledge and expertise at Stamford Bridge once again."