Uruguay forward had been expected to sign for los Blancos during the close season.
Unsettled Liverpool front man Luis Suarez is set to join Chelsea this summer in a deal worth a reported £34 million, says the Daily Star.
The controversial Uruguay international has been the subject of intense speculation of late linking him with a possible big-money move away from Anfield when the transfer window reopened on July 1.
However, it had been thought that the 26-year-old would be joining Spanish giants Real Madrid next season, especially after the player himself had declared his wish to play at the Santiago Bernabeu while away on international duty at the recent Fifa Confederations Cup in Brazil.
But according to reports in Spanish sports daily AS on Saturday the striker, who has netted an eye-catching 51 goals and 24 assists in just 96 matches for the Reds since arriving on Merseyside from Ajax in Jan 2011, is actually now on the verge of completing a stunning £34m move to Stamford Bridge instead this summer.