The Spain international left the Reds to join Real Madrid in the summer of 2009, and the Anfield outfit quickly lived to regret the sale.
The club have been struggling to return to old glory days ever since, but they have never given up hope of luring Alonso back to Anfield.
Liverpool have been showing signs of promise this season and with captain Steven Gerrard set to sign a new deal, the Reds hope Alonso might be interested in a return.
The 31-year-old has a contract until June 2014 at Santiago Bernabeu and he has been unable to reach an agreement with club chiefs over a contract extension.
Liverpool are closely monitoring the situation and they are ready to pounce should the player decide to leave his current employers at the end of he season.