The Merseyside club lead Manchester City at the top of the Premier League table with two points albeit having played a game more.
"The title race will go down to the wire, there is no doubt about that," Rush told Sky Sports News.
"There are just a few games to go and as long as they keep winning they are one step closer, but I think they are starting to believe now that it can be done.
"People are saying all the fans are getting excited, but why not? Why shouldn't they be excited? If they don't get excited now, they'll never get excited!
"The most important thing is that the players - with the help of the coaching staff and the manager - keep their feet on the ground.