Real are trying to trim their squad after a 250 million euros ($358.4 million) spending spree on a number of top players including Cristiano Ronaldo, Kaka and Xabi Alonso.
They have a dearth of midfielders and, according to media reports in Spain and Italy, have been negotiating a deal to sell Sneijder to Inter Milan.
"I want to play at Real Madrid. I don't want to leave because I know I am capable of being an important part of this team," Sneijder was quoted as saying in sports daily Marca.
"I will fight until the very last moment to stay here. I will continue to train hard like a good professional so they see I am keen to continue here."