Cheyrou has made a fine start to his Anfield career, scoring Liverpool’s second in last week’s 5-0 defeat of Spartak Moscow.
But while Houllier is happy with the midfielder’s progress he believes that Cheyrou is still learning and has a way to go before emulating the success of Zidane.
He said: "To me, Bruno has some of the attributes of Zinedine Zidane, he has his ability to pick a pass, and moves a little like him.
"Zidane is 29 and at the very peak of his game, while Bruno is just a youngster, and is still very much learning, especially about English football."
"Look at Pires and Wiltord. They took time, because the Premiership is so different to France. It is so much quicker and more physical. But look at them now."
And Houllier believes that for Cheyrou to fulfill his promise he must add a mean streak to his game.
"Bruno has got great skill and he’s got an eye for a pass.
"I would say he’s a combination of Jamie Redknapp and Gary McAllister - that’s why I bought him.
"He does need to strengthen up his game and become a little bit tougher. That is often the case for new players to the English game."