The Uruguayan striker was heavily linked with the La Liga giants last summer, and even agitated publically for the move.
Liverpool held firm despite his desire to leave, and have since rewarded him with a bumper contract and secured the Champions League football he craved – during which time he has netted over 30 Premier League goals and won the PFA Player of the Year award.
But this has not deterred Real, who are ready to pay upwards of £60m for the forward.
Los Blancos chief Florentino Perez is said to have made Suarez his top target to complete a terrifying forward three with Gareth Bale and Cristiano Ronaldo – who cost over £160m combined – as he seeks to land a top class goal-getter.
Real are keen to open the bidding before the World Cup starts, and are aware that other top clubs such as PSG and Manchester City may get involved.
Liverpool are liable to resist any move for the star man, and have been buoyed by the player’s recent admissions of his happiness on Merseyside and eagerness to experience Champions League football at Anfield.