Italy striker Balotelli has failed to make an impact since arriving at Anfield from Milan in August.
Serie A champions Juve have been linked with a January swoop for the enigmatic striker, but Allegri denied any interest in signing a player who he knows all about from his time at Milan.
He told Italian TV station RAI: "I think this is a made-up story.
"Balotelli has done very well with me but he belongs to Liverpool and he is not a player that can arrive at Juventus."
Balotelli's representative, Mino Raiola, expects the former Manchester City forward to come good for Liverpool.
He told RAI: "I'm not worried, Mario has been out for almost 10 weeks with an injury and you cannot judge him until he is 100 per cent fit.
"It's not easy to go abroad and adapt quickly to a new team."
Raiola also insisted that he had no regrets over Balotelli's Milan exit.
"Decisions are judged at the time when they are made, In the summer, it was right to leave Milan and I would do it again," he added.
"Mario has gone to the best league in the world. Now he is not doing well at Liverpool for different reasons but Mario is calm and he is working to return to be in top condition.
"I do not regret this transfer and Mario's departure from Milan."
