Suarez, who had been the subject of interest from Real last summer, stayed on at Liverpool after signing a new long-term contract.
However, Real are ready to push ahead with a deal to bring the Uruguayan international to Spain this summer after Suarez has enjoyed a remarkable season helping Liverpool to compete for the Premier League title, Metro.co.uk reported.
Real president Florentino Perez reportedly wants to add a big name Galactico forward to the squad next season to compete on all formats and Suarez has been made the number one choice.
Media reports have revealed that Real would start the bidding at 60 million-pounds before the World Cup kicks off next month, but they can even go higher to get the striker.
Liverpool will reportedly resist any offer for their leading striker, but Suarez is speculated to be keen on a move to Real and might find it difficult to resist a switch.
However, if a cash deal cannot be reached, Real could use their striker Karim Benzema, who is about to enter the final year of his contract at the club, as a make-weight for the Uruguayan international, the report added.