However, Benitez is happy with The Reds' two third-placed finishes in the last two seasons and has told Allardyce to worry about his own business on Tyneside.
"I want to say two things," Benitez told the club's official website . "Firstly, I think he should be more worried about his own business because he must have more problems than to waste time talking about other managers.
"Secondly, has he forgotten Liverpool winning the Super Cup, FA Cup and Champions League as well as reaching another Champions League final, a Carling Cup final and twice finishing third in the Premier League?
"Maybe he doesn't have a great memory."