The Colombian has made just eight LaLiga appearances this season and coach Zinedine Zidane has suggested he might not feature again in 2019-20.
He was linked with a switch to Atletico Madrid last summer, while Napoli and AC Milan were interested, too, but Los Blancos opted to keep him.
Rodriguez discussed his failed move to Atleti in an interview with former England international Rio Ferdinand.
"Last summer I got a really good offer from a club I won’t name," the 29-year-old revealed.
"But I wanted to go there because I knew I wouldn’t play much here [Real Madrid]. I got the offer from this club, but I wasn’t allowed leave due to a number of reasons.
"So, basically I’m here this year because of the circumstances, not because I wanted to be, because I knew that I wouldn’t be able to play much."
Madrid are unlikely to keep him this year, however, and he is determined to find a new club this summer.