The Uruguay midfielder has become disillusioned after making only 20 La Liga appearances for Diego Simeone's side last season.
Rodriguez, 28, believes the time has now come for him to seek a transfer ahead of the new season.
He told Radio Sport 890: "Every footballer wants to play as much as possible and what I want is a team in which I can have more minutes on the pitch and which has confidence in me.
"I have to leave, it's not that I want to leave. I am very comfortable in Madrid.
"At my age, the best thing is to play more. If I stay another year the same situation is going to get repeated, so my idea is to leave."
Rodriguez started all four games for his country at the World Cup in Brazil.