The 28-year-old has been with the Spanish side since 2012, but has struggled to hold down a regular first-team role with the capital outfit this season.
Despite being a regular member of the squad, the Uruguayan has been restricted in terms of starting appearances and he has confirmed that he will seek pastures new in the summer.
"Every players wants to play and what I want is that can give me more minutes, where I can be a starter, a team that relies more on me," he told Sport 890.
"I have to go, it's not that I want to go. I am very comfortable in Madrid. At my age, ideally, I have to play more. If I stay another year, the same thing is going to repeat itself and my idea is to leave."
Rodriguez is expected to be part of the Uruguay squad that travels to the World Cup this summer.