The Monaco attacker scored six times for his country at this summer's World Cup, with that total, as it stands, enough to gain him the Golden Ball.
Interest has intensified following an impressive summer display and now Rodriguez has added fuel to the fire when asked about a possible move to Los Blancos.
"It would be a dream to play for Real Madrid but at the end of it all, I respect my club who has the final say," he told Marca.
"I respect all the other teams, fans and players of other clubs but Real Madrid will always be Real Madrid. It makes me profoundly proud that a club like Real Madrid is interested in me. It's like a dream.
"I feel calm because I know I can play in a club like Real Madrid. I've been to the Bernabeu once and it was amazing. I told myself I wanted to play here one day. Dream to play for Real Madrid? It's obvious all the players dream to play for Real Madrid."
Rodriguez joined Monaco from Porto just last summer.