Rush told The Sun: "When you look at what's happening at other clubs, why shouldn't Liverpool go close? I just hope Rafa gets the money to sign Barry and Keane - then I could see them giving it a real go.
"If they get support, I can see them mounting a genuine push - and not before time.
"It's no good setting your sights on fourth at a club like this, where expectations are so high.
"And maybe this is the right time. United have lost No 2 Carlos Queiroz and no-one knows what will happen with Cristiano Ronaldo.
"Chelsea have a new boss and new players but even great ones need time to gel.