The former Chelsea striker believes the Italian is talented enough to be a success on Merseyside.
Balotelli made his debut in the Reds 3-0 win over Tottenham at White Hart Lane on Sunday following his £16 million switch and Shevchenko believes the Italian is at a club with the ambition to compete for Europe's big prize.
Goal picked up on quotes from Gazzetta dello Sport, where Shevchenko said: "If Balotelli wasn't happy at Milan and the club were not satisfied either, it was the right decision to part ways.
"But I saw Mario in action at the European Championship in Ukraine and Poland two years ago and he was a fantastic player. I refuse to believe that's all gone all of a sudden.
"Mario deserves another chance and Liverpool are giving him that chance. Liverpool are a great team and could have the ambition to win the Champions League.
"It's now up to Balotelli to overcome his difficulties and take his fate back in his own hands again."
Despite not getting on the scoresheet on his debut for the Reds, Balotelli pleased both his new manager and fans. He seemed to link up the play well, was a threat in the penalty area and probably surprised a lot of people by showing his willingness to track back and help out with the side's defensive duties.
Balotelli was recently overlooked for the Italian national side and will feel he has a point to prove in the coming weeks, which is something that Liverpool will no doubt hope to use to their advantage.