The Uruguayan has recently pledged his future to the Reds, but former Los Blancos president Ramon Calderon says that he would not be surprised if the newly-crowned European champions make a move for the 27-year-old, as a possible replacement for Karim Benzema.
He told the Daily Star: "Luis Suarez, no doubt, is one of the best players in the world and he's had a fantastic season with Liverpool.
"Of course Real Madrid could bid for him. With Real Madrid, you have to expect anything – that's for sure.
"Benzema is a good player but it's true he didn't score as many goals as people thought he should."
Suarez is hopeful of playing a part in Uruguay's World Cup campaign, starting next month, despite undergoing surgery on a knee injury.