"A lot of things are said about me and almost all of them are lies," Rodriguez told Gol Caracol. "What makes me most uncomfortable is when people doubt my professionalism. I can't accept that. I'm very professional, that's why I've got as far as I have. People who've worked with me know what I'm talking about. I take care of myself as much as anyone."
The 28-year-old was initially a regular starter when Real Madrid signed him for €75 million from AS Monaco in 2014, after top scoring at that year's World Cup.
Since then, his Bernabeu career has stalled, spending two years on loan at Bayern Munich and making just five La Liga starts since returning last summer.
"It's a good question, I'd like to know too," Rodriguez said when asked why he hasn't played more often. "As I've said before, when you win trophies with players you trust and you have a settled team, it's difficult to change. It's also complicated when your coach doesn't give you minutes. It's hard to show what you can do."
"There hasn't been any kind of problem [with Zidane]," he added. "Each coach has his preferences. We have a normal working relationship... I'm not one of the key players, that's clear. I'm training and working so that when it's my turn, I do well."
"In the future who knows what is going to happen," he said. "If I were able to choose, I'd pick a club where I can show my ability and my quality."
Sources close to the player have told ESPN that the Premier League or Italy's Serie A are more likely destinations than MLS at this stage of his career.
Rodriguez admitted that his preference last summer was to join another La Liga club, thought to be Atletico Madrid.
"There was a really good offer from a Spanish team which Real Madrid rejected. I started pre-season with Madrid without wanting to," he said. "I also had an offer from Italy but it didn't convince me. My agent Jorge Mendes told me Real Madrid had an offer from China, but I wasn't ready to go there because I feel I can give a lot more in Europe."