Rush said: "Liverpool are not far away from having a championship-winning side. There can be no doubting the huge potential in the Liverpool squad. And with world-class players like Michael Owen, Steven Gerrard and Sami Hyypia, they have the quality to match the top two.
"But Liverpool are a very young side. Maybe they could do with an influential acquisition capable of having the same impact Gary McAllister provided. Manchester United have Roy Keane, David Beckham and Ryan Giggs as standard-bearers.
"Arsenal can call on the old heads of Dennis Bergkamp, Martin Keown and David Seaman. Newcastle have benefited from the guile of Alan Shearer and Chelsea can turn to Marcel Desailly and Gianfranco Zola.
"Liverpool have a much younger pool of players who will only get better. People like El-Hadji Diouf, Milan Baros and Bruno Cheyrou will benefit from their first season in the Premiership. But a player with an old head can make a big difference."