The 28-year-old has only made 14 appearances for Los Blancos this season and continues to be linked with a move away from the Bernabeu ahead of this summer's transfer window.
Rodriguez's off-the-field conduct has been called into question amid the speculation surrounding his future, but the Colombia international has insisted that he has never behaved in an unprofessional manner.
"It's always uncomfortable to listen to the many lies that are said about someone, what's important is the opinion of my family and those who know me," Rodriguez told Gol Caracol.
"Anyway, it's something that doesn't affect me because I know what's true and I work hard every day to be where I am. Those who surround me are always happy with what I have to offer.
"A lot of things have been said about me and almost all of them are lies. What most annoys me is that my professionalism has been put in doubt, and I can't accept that. I am very professional, that's why I got where I am now.
"It's reassuring that the people that are by my side and worked with me know what I'm talking about. I take care of myself like nobody else. I train a lot in my day to day. I always want to improve."