Balotelli made a £16m move to the Reds last month, and much has been made about the Italian's temperament.
Hamann, who won the 2005 Champions League with the Reds, thinks that the former Manchester City forward still has to show that he can co-exist with his teammates.
"He still needs to prove that he is a team player, because everywhere he's been so far, he's caused trouble," Hamann told Sky Sports News.
"There's no doubt that he's a fantastic talent, and for £16m you've got to say he's a bargain."
Balotelli is expected to make his Anfield debut against Aston Villa on Saturday.