Shevchenko joined Chelsea from AC Milan for £30million last summer, but has only scored four league goals for the Blues.
Voronin said: “I spoke to Shevchenko about coming to Liverpool and he remains one of the great strikers in Europe.
“He didn’t perform as well as he was expected to last season.
“But he played in Italian football for seven seasons with AC Milan and that league is totally different to the English game.
“Maybe he just needed a little more time to get used to the English style.
“I think he’ll do better this season because he is a goalscorer.”