The Uruguayan international publicly expressed a desire to leave Anfield in the summer and was linked with a move to Madrid, with Arsenal also making an approach. However, the Reds were keen to keep Suarez at the club and Liverpool's chiefs rejected bids from the Gunners.
Madrid were believed to be interested in landing the former Ajax man in the summer, but their main focus was on signing Gareth Bale, who completed his world record move to Santiago Bernabeu from Tottenham Hotspur.
The Daily Mail claims that the Merseyside club is aware of Madrid's growing interest in Suarez and expect to receive a £45m bid for the striker. However, Liverpool will demand a fee of £55m before letting their star player leave during the mid-season transfer window.
An earlier report suggests that Suarez's agent Pere Guardiola is already holding talks with the Spanish giants over a possible transfer to Madrid in the January transfer window. The 26-year-old is still keen on joining the nine-time European champions, despite being forced to continue with his current employers.
Madrid allowed Gonzalo Higuain complete his switch to Napoli in the summer. This has left Carlo Ancelotti with Karim Benzema as the first choice striker, with Alvaro Morata and Jese Rodriguez providing cover.
Benzema has been criticised for a string of his poor performances. The former Chelsea boss has even confirmed the Frenchman will be replaced by Morata for the weekend league fixture against Levante, citing squad rotation as the reason behind dropping the striker to the bench.
Suarez served his 10-match ban for biting Chelsea defender Branislav Ivanovic and scored twice in his first league game of the season against Sunderland. The striker's compatriot Edinson Cavani has revealed that the Liverpool star still has his heart set on joining Madrid, despite committing his future to the Reds.
"I am sure Liverpool fans are very happy Luis stayed - he will be a big player for them. I think Arsenal was not Luis's dream move, maybe if it had been Real Madrid then it would have been a different outcome - but of course Madrid were concentrating on a different target this summer," Cavani said.
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