The Anfield club's American owners sacked their director of football ahead of the FA Cup semi-final victory over Everton because they were unhappy that a big-spending approach had not resulted in any progress in the Premier League.
They were linked with Ajax and Barcelona great Johan Cruyff, but found the Dutchman had no interest in moving to England.
Instead, he recommended the Liverpool board to consider Begiristain for the vacancy, reports the Metro.
If Begiristain, who played a part in building the current Barcelona team by bringing in Dani Alves, David Villa and Gerard Pique, was handed the job, he would look to implement a change in the recruitment strategy at Anfield and the focus would be very much on players under the age of 21.
This story has been reproduced from the media. It does not necessarily represent the position of Liverpool Football Club or Red's Fury™ blog.
Stay tune for more news and follow me on Twitter.