Manchester United will hit the league summit for the first time this season if they win at Bolton on Saturday, with Liverpool not in action until Monday night when they entertain Everton at Anfield.
But Rush feels Liverpool finally have the strength in depth to finally win their first Premier League crown.
Speaking exclusively to FourFourTwo.com, the former Wales forward said: "They've spent quite a bit of money and have more depth than before. People say that without [Steven] Gerrard and [Fernando] Torres they aren't good enough but they beat Manchester United without Torres and Gerrard and beat Chelsea at Stamford Bridge without Torres, so I think that goes to show that they've got the depth to make a real challenge.
"The players have to start believing they can win it, they're in a better position now than they were in August and there's no reason why they can't see it through."
The Reds dropped points against newly-promoted Stoke for the second time this season last weekend, with some pundits claiming the team were affected by, manager, Rafa Benitez's extraordinary rant at Sir Alex Ferguson during his pre-match press conference last Friday.
However, Rush is quick to defend the Spaniard's attack at the Manchester United boss.
"I don't really see the problem. If Rafa's got the facts I think he's quite entitled to state them to whoever he wants, all he was really doing was standing up for himself and the club.
"I don't think mind games are as big a factor as the press sometimes make out. Ferguson tried it with Kenny Dalglish in the past and it didn't work. It will only affect you if you believe in it all; if you don't it means nothing."
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