A number of bids were received for Rodriguez, who made just eight La Liga appearances for Madrid in the first half of the season, but after being given the nod to start against Napoli in midweek he has now changed his tune.
"I think everything is going well - Madrid are a big club and I always wanted to be here," he is quoted as saying by the Daily Mail. "Good and bad things always happen but I want to stay here for a lot longer.
"I always train to play and I want to be here. You always want to play, now that I have more game time, everything is slowly changing."