Balotelli sealed his £16m move from AC Milan on Monday but the transfer was not completed in time for him to feature against former club Manchester City later in the evening.
However, the Italy striker is now available for selection to face Tottenham on Sunday after he was forced to watch the 3-1 defeat at the Etihad Stadium from the stands.
Manager Rodgers told the club's official website: "I think by the weekend [he'll be ready to feature].
"He's been into pre-season and he's played three 45-minute games. He might not be up to full match speed, but he's looking fit.
"We've done some analysis on him. The medical and sports science team have worked with him already and he's in very, very good condition.
"He's in to work and he'll be available for the squad for the weekend."
You can watch Tottenham v Liverpool on Sky Sports 1 on Sunday at 1.30pm