According to Metro.co.uk, the Uruguayan 's future was one of the main talking points of the summer with the 26-year-old claiming he wanted out of Anfield after the Reds failed to qualify for the Champions League  last season.
Arsenal failed in two attempts to prise Suarez away from Liverpool, while Madrid were also keen but couldn't justify spending the cash after splashing 85 million pounds on Gareth Bale, the report said.
However, Real are now ready to bid for the striker after being told by his agent, Pere Guardiola, he remains keen on a move to La Liga, the report added.
The Spanish giants aim to raise the money by off-loading Angel Di Maria, a possible target for Arsenal, the report further said.
Suarez has insisted he is now happy to stay at Anfield, following Liverpool's impressive start to the Premier League season, but the lure of Madrid would prove very hard to turn down, according to the report. (ANI )