The Italy international has scored just two goals since joining Liverpool from AC Milan in a 16million transfer in August and has yet to find the back of the net in the Premier League this season.
Allegri, who coached Balotelli at Milan before taking the helm of Juve in July, 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."
The 24-year-old Balotelli, who is a reported target of Paris St Germain, has struggled with a groin injury since November.
Balotelli's agent Mino Raiola insists that despite Balotelli's slow start to life at Anfield, the former Inter Milan striker will come good at Liverpool.
"I'm not worried," Raiola told RAI
" 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 does not regret Balotelli's return to the Premier League.
The striker played almost three seasons at Manchester City before joining AC Milan in January 2013.
"Decisions are judged at the time when they are made," Raiola said
"In the summer, it was right (for Balotelli) to leave Milan and I would do it again.
"Mario has gone to the best league in the world.
"Now he is not doing well at Liverpool for different reasons b ut 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."
Balotelli is under contract with Liverpool until June 2017.
Source: PA