However, despite the speculation, the 27-year-old has reassured supporters of Los Blancos that he will continue to give his all for the club.
"That I am feeling sad and have expressed this sadness has created a huge stir," he wrote on Twitter. "I am accused of wanting more money, but one day it will be shown that this is not the case.
"At this point, I just want to guarantee to the Real Madrid fans that my motivation, dedication, commitment and desire to win all competitions will not be affected.
"I have too much respect for myself and for Real Madrid to ever give less to the club than all I am capable of. Abrazos to all Madridistas."
The number seven joined Madrid in 2009 from Manchester United for a world record fee of £80m.