According to reports in Spain [via Mirror Sport] the former Real Sociedad deep-lying playmaker has been told by ex-Reds boss Rafael Benitez that he has no future at the Santiago Bernabeu and is free to look for a new club before the transfer window shuts next month.
Illarramendi has found it very difficult to establish himself at the club since his arrival in the summer of 2013 for a fee believed to be in the region of £34million [via BBC Sport] and started just 10 La Liga games for Los Blancos last season.
The 25-year-old is reportedly available for £14.2million and that could entice Reds manager Brendan Rodgers into making a bid as he looks to further bolster his squad ahead of the new Premier League season.
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The Merseyside outfit have been extremely busy in the transfer market so far as James Milner, Adam Bogdan, Danny Ings, Joe Gomez, Roberto Firmino, Nathaniel Clyne, Christian Benteke and youngster Allan Rodrigues de Souza have all joined the club over the summer.